UC-NRLF 


B    M    En    Ifib 


IThe  Effect 

Discrimination 


FRANKLIN  ORION  SMITH 


t^ 


Reprinted  from   Psychological  Review  Monograph   No.  69 


The  Effect  of  Training  in  Pitch 
Discrimination 


FRANKLIN  URION  SMITH 


I 


Reprinted  from  Psychological  Review  Monograph  No.  69 


The  Effect  of  Training  in  Fitch 
Discrimination 


FRANKLIN  ORION  SMITH 


A  thesis  submitted  to  the  Department  of  Philosophy  and  Psy- 
chology of  the  Graduate  College  in  the  State  University  of 
Iowa,  in  partial  fulfillment  of  the  Requirement  for  the  degree 
of  Doctor  of  Philosophy. 


Ml- 


&^ 


BERKELiY 

MUSIC  LIBRARY 

UNIVERSiTV  OF 
CALIFORNIA 


1 


THE  EFFECT  OF  TRAINING  IN  PITCH  DISCRIMINATION 

BY 
FRANKLIN  ORION  SMITH 

CONTENTS 

Method  of  procedure 

Effect  of  instruction 

Effect  of  practice 

Factors  in  the  development  of  pitch  discrimination 

The  psychological  limit 

Correlations 

General  conclusions 

The  present  investigation  forms  a  part  of  a  series  of  researches 
in  the  Iowa  laboratory/  upon  the  tonal  hearing.  The  problem  was 
to  determine  the  effects  of  training  in  tonal  hearing,  considering 
age,  sex,  musical  education,  general  intelligence,  and  kinship. 

The  investigation  consisted  of  a  preliminary  training  series,  a  ten 
days'  practice  series  and  the  correlation  of  the  results  with  those  of 
other  researches.  The  experiments  were  conducted  in  the  Univer- 
sity and  in  the  public  schools  of  Iowa  City  and  Cedar  Rapids  in 
1908- 19 1 2. 

Method  of  procedure 

The  tuning  forks  and  accessories  which  were  employed  in  this  re- 
search are  fully  described'  by  Professor  Seashore  in  his  report  for  the 
American  Psychological  Association  on  the  standardizing  of  pitch 
discrimination  tests.-  The  experimental  precautions,  both  subjec- 
tive and  objective,  were  observed  as  set  forth  in  that  report.  The 
only  change  made  in  the  apparatus  consisted  in  using  two  resonators 
instead  of  one,  which  is  a  decided  improvement  because  one  resona- 
tor alone  does  not  speak  sufficiently  well  at  the  extremes  where  in- 
crements as  large  as  23  or  30  v.d.  are  used.  The  methods  of  pro- 
cedure recommended  in  the  above  named  report  were  followed,  as 

^  The  writer  wishes  to  acknowledge  his  manifold  indebtedness  to  Pro- 
fessor Seashore  for  his  supervision  and  cooperation,  which  have  made  this 
research  possible.  To  Dr.  Mabel  C.  Williams  and  to  companions  in  research 
who  are  working  upon  related  problems  in  the  laboratory,  he  expresses  his 
grateful   appreciation   for  assistance. 

^  Psychol.  Monog.   No.  53. 


^y-^iBO 


68  FRANKLIN  O.  SMITH 

described  on  pages  39-43  of  that  report.  The  "heterogeneous" 
method  was  used  in  all  preliminary  experiments  and  with  unclassi- 
fied groups.  This  consists  in  presenting  the  increments  30,  23,  17,  12, 
8,  5,  3,  2,  I,  and  .5  v.d.  in  the  order  named  a  number  of  times  and 
finding  at  what  level  in  that  series  the  threshold  falls  in  from  ten 
to  twenty  trials.  The  mean  variation  of  the  records  for  all  such 
sets  is  then  computed  by  the  method  described  on  page  42  of  the 
above  named  report,  as  follows : 

"For  ordinary  work  we  threfore  recommend  as  a  measure  of 
variation  in  the  record  the  use  of  the  mean  variation  (m.v.)  com- 
puted as  follows :  Regard  the  difference  between  successive  steps 
as  equal  psycho-physic  steps  and,  with  the  increment  which  is 
nearest  to  the  median  as  a  base,  multiply  the  number  of  cases  which 
are  one  step  from  this  base  by  i,  the  number  that  are  two  steps  away 
by  2,  the  number  that  are  three  steps  away  by  3,  etc. :  divide  the 
sum  of  these  products  by  the  total  number  of  cases  (sets)." 

The  homogeneous  method  is  the  ordinary  method  of  right  and 
wrong  cases  or  constant  stimuli,  counting  the  threshold  at  75  per 
cent,  corrected  cases.  This  method  was  used  in  dealing  with  indivi- 
duals or  groups  formed  on  the  basis  of  preliminary  tests. 

The  preliminary  training  consisted  of  two  tests  which  are  desig- 
nated as  the  first  and  second  preliminary  tests  respectively.  The  ob- 
servers consisted  of  pupils  in  the  elementary  and  high  schools,  and 
students  in  the  University.  The  ages  vary  from  nine  years  to  ma- 
turity. Most  of  the  observers  were  unmusical  in  the  sense  that  they 
had  received  no  special  training  in  music.  These  tests  were  made 
in  the  schoolrooms  under  good  conditions.  The  temperature  and 
ventilation  were  regulated  by  automatic  systems  (except  in  two 
small  grade  schools).  The  regular  teacher  remained  in  the  room 
during  the  experiment  maintaining  normal  conditions  of  order  and 
school  spirit.  These  general  conditions  did  not  differ  materially 
among  the  schools  nor  among  the  different  rooms  of  the  same  school. 
The  tests  were  carried  on  in  the  morning  between  nine  and  twelve 
o'clock,  each  test  lasting  twenty  to  twenty-five  minutes. 

Since  it  was  not  practicable  in  all  cases  to  employ  the  homogeneous 
method,  all  the  group  tests  were  made  by  the  heterogeneous  method 
In  figuring  the  results  the  nearest  whole  vibration  (except  0.5  v.d.) 
was  taken.  The  increments  in  the  series  of  tones  used  (0.5,  i,  2,  3, 
5,  8,  12,  17,  23  and  30  v.d.)  are  referred  to  as  units  and  are  con- 


EFFECT  OF  TRAINING  IN  PITCFI  DISCRIMINATION         69 

■sidered  equally  difficult  to  distinguish.  That  is,  23  to  30  v.d.  is 
assumed  to  be  as  difficult  for  one  whose  threshold  is  23  v.d.  as  i  to 
2  v.d.  is  for  one  whose  threshold  is  i  v.d. 

In  case  of  defective  hearing  the  pupil  was  seated  where  he  would 
be  certain  to  hear;  or,  if  the  deafness  was  serious,  he  was  excused 
from  the  test.  The  rhythm  of  the  work  period  was  not  so  easily  con- 
trolled. The  tests  were  comparatively  short  and  every  effort  was 
made  both  by  the  experimenter  and  the  attending  teacher  to  keep 
the  effort  up  at  a  high  pitch  throughout  the  test.  Indifference  is 
perhaps  the  largest  source  of  error  in  the  few  cases  where  it  was 
manifest.  This  could  be  recognized  directly  at  the  time  of  the  test 
and  usually  also  by  the  distribution  of  errors  in  the  records. 

One  of  the  most  striking  and  yet  perplexing  facts  about  pitch  dis- 
crimination is  that  there  is  often  no  relation  between  the  feeling  of 
certainty  and  the  correctness  of  the  judgment.  The  judgment  is 
often  based  upon  a  clear  illusion.  This  illusion  of  hearing  in  the 
case  of  wrong  judgment  aids  much  in  the  encouragement  to  sus- 
tained effort. 

Anticipatory  judging  is  a  fruitful  source  of  errors.  Under  the 
influence  of  expectant  attention  the  observer  anticipates  the  second 
tone  the  moment  he  hears  the  first.  The  experience  is  analogous  to 
the  illusion  of  lifted  weights.  With  a  strong  expectation  of  hearing 
the  second  tone  high,  or  low,  the  organism  is  set  to  make  the  ap- 
propriate response  and  this  has  marked  influence  upon  the  judgment. 
Closely  related  to  anticipatory  judging  is  the  tendency  to  compare 
the  present  tone  with  the  preceding  pair.  In  fact  this  tendency  often 
leads  to  anticipatory  judging  especially  when  the  first  tone  of  the 
present  pair  is  compared  immediately  with  the  last  tone  of  the  pre- 
ceding pair. 

The  confusion  of  pitch  and  intensity  is  a  troublesome  source  of 
error,  particularly  with  unpracticed  observers.  Making  the  tones 
actually  objectively  equal  in  intensity  does  not  always  allay  the  diffi- 
culty as  disturbing  associations  may  tend  to  create  confusion.  High 
tones  are  intrinsically  louder  than  low  tones.  A  slight  difference  in 
intensity  is  often  interpreted  as  a  difference  in  pitch. 

In  computing  the  characteristic  figure  of  a  record  it  is  necessary  to 
take  account  of  internal  evidences  and  make  a  "correction"  as  is 
explained  in  the  report  of  this  test  referred  to  above,  pages  45-48. 
This  must  always  be  a  matter  of  "good  judgment"  and  can  not  be 


70  FRANKLIN  O.  SMITH 

done  mechanically.  Certain  factors  may  however  be  quite  clear  and 
exact.  The  distribution  of  the  records  in  the  heterogeneous  test  with 
respect  to  the  operation  of  the  laws  of  chance  is  one  of  the  most  tell- 
ing. A  record  of,  e.g.,  8  v.d.  may  on  examination  of  the  distribution 
of  the  errors  be  found  to  contain  indisputable  proof  of  a  threshold 
of  2,  or  I,  or  .5  v.d.  as  the  case  may  be. 

Sometimes  when  a  source  of  error  has  been  noted  a  study  of  the 
distribution  may  show  where  it  operated  and  where  it  did  not  oper- 
ate. A  small  mean  variation,  e.g.,  i.o  or  less  is  almost  certain  proof 
of  the  reliability  of  the  actually  computed  median.  The  study  of  the 
internal  evidences  therefore  has  its  principal  use  in  cases  showing  a 
large  mean  variation.  All  our  records  were  examined  with  reference 
to  internal  evidence  of  error  in  the  computed  median  and,  it  must  be 
frankly  admitted,  wherever  such  evidence  was  found  the  correction 
was  made.  All  the  records  here  used  in  the  heterogeneous  method 
are  therefore  "corrected"  records.  Fig.  i  shows,  it  will  be  seen,  that 
the  tendency  of  the  correction  is  to  lower  the  record  and  that  most 
of  the  corrections  are  made  for  those  who  have  poor  records. 


«*^-*      '      2      y      y 5 — a — 79 — 73 — Iff 

Fig.  I.     Distribution  of  476  pupils  for  one  day's  practice  before  and  after 
the  records  had  been  corrected. 


The  effect  of  instruction 

As  a  preliminary  to  the  training  series  two  tests  of  about  25 
minutes  each  were  given  to  1980  pupils  by  the  heterogeneous  method 
in  their  regular  class  divisions.  In  the  first  period  the  test  was 
begun  without  any  explanation  beyond  what  was  necessary  to  direct 
them  about  reporting  "higher"  or  "lower".  The  second  period  was 
opened  with  simple  and  diversified  explanations  and  illustrations  of 
what  pitch  is.  This  explanation  was  based  upon  a  previous  study 
of  the  kinds  of  difficulties  encountered.     Pitch  was  differentiated 


EFFECT  OF   TRAINING  IN  PITCH  DISCRIMINATION         71 

from  intensity,  duration,  volume,  timbre,  etc.  in  familiar  talk  and 
by  different  instruments. 

Unfortunately  the  two  factors  of  instruction  and  experience,  or 
direct  observation  resulting  in  a  growing  familiarity  with  the  prob- 
lem, are  not  isolated.  We  have  simply  the  records  for  the  two 
periods  and  must  interpret  the  gain  as  due  to  both  of  these  factors, 
which  are,  of  course,  inseparably  associated. 

To  facilitate  comparison  the  observers  were  divided  on  the  basis 
of  these  tests,  into  A,  B,  and  C  grades  in  accordance  with  the  posses- 
sion of  a  good,  medium,  or  poor  ear.     Grade  A  includes  those  who 


TABLE  I.    D 

istribh 

'.tion  of 

■  those 

'  who 

improved  in 

the  p 

reliminary  te 

St 

30 

23 

17 

12 

8 

5 

3 

2 

I 

0.5 

A 

B 

30+ 

II 

II 

10 

15 

6 

3 

2 

I 

0 

0 

59 

23 

17 

12 

8 

5 

3 

2 

/ 

0.5 

30 

13 

13 

II 

17 

7 

3 

0 

0 

0 

64 

II 

17 

12 

8 

5 

3 

2 

I 

0.5 

23 

13 

\2 

15 

2 

3 

0 

0 

0 

45 

24 

12 

8 

5 

3 

2 

I 

0.5 

17 

17 
8 

38 

5 

14 
3 

4 
2 

I 

I 
0.5 

I 

76 

36 

12 

25 

5 

30 

3 

16 

3 

/ 

I 
0.5 

75 

55 

8 

103 
3 

43 
2 

15 

10 

0.5 

0 

171 

lOI 

5 

126 
2 

35 

8 
0.5 

8 

177 

159 

3 

122 

45 
0.5 

13 

180 

197 

2 

44 
0.5 

7 

51 

177 

I 

9 

9 

147 

Italics  designate  increments;  the  other  figures  give  the  number  of  cases 
for  each  of  the  respective  degrees  of  improvement;  thus,  of  those  who  had 
a  record  of  304-  in  the  first  test,  11  went  to  30—,  n  to  23,  10  to  17,  i5  to 
20,  6  to  8,  3  to  5,  2  to  3,  and  i  to  2  in  the  second  tes't.  A  shows  the  total 
number  of  cases  at  each  increment  in  the  first  test ;  B  same  in  second  test. 

hear  differences  of  less  than  3  v.d. ;  grade  B  those  who  hear  differ- 
ences of  3  to  14  v.d. ;  and  grade  C  those  who  hear  differences  of 
14  to  30  v.d.  or  above. 

The  records  show  that  54  per  cent,  made  no  improvement  in  the 
second  test;  46  per  cent,  of  all  observers  made  better  records  in  the 
second  preliminary  test  than  in  the  first.  The  amount  gained  varies 
from  I  to  8  units.  The  average  amount  gained  varies  from  3.8  v.d. 
at  nine  years  of  age  to  0.3  v.d.  at  maturity. 

Table  I  analyzes  the  distribution  and  the  amount  of  gain  by  the 


72 


FRANKLIN  O.  SMITH 


cases  (46  per  cent.)  which  improved  with  the  instruction.  Of  the  46 
per  cent,  who  improved,  only  7  per  cent,  changed  from  grade  C  to 
grade  A  in  the  second  test.  Of  the  425  pupils  (22  per  cent.)  who 
improved  and  were  in  grade  B  at  the  beginning,  225  (60  per  cent.) 
changed  to  grade  A  in  the  second  test.  Measured  by  the  first  test 
26.5  per  cent,  of  those  who  improved  were  in  grade  A.  Measured 
by  the  second  test  70  per  cent,  were  in  grade  A.  Of  the  changes  to 
grade  A,  96  per  cent,  were  from  grade  B ;  and  91  per  cent,  of  the 
changes  to  grade  B  were  from  grade  C. 


Fig.  2.     The  effect  of  instruction.     Distribution  of  907  pupils  who  made 
improvement  from  the  first  to  the  second  preliminary  test. 


.fJret  fesM, 


OS      f        a        J        s        o        iz       17       23      30      yj* 
Fig.  3.     Distribution  of  entire  group,  1980  cases,  in  preliminarj'  tests. 


n      13     lb  f 


^fe     io      11      /2      /5      /9      7s      ie 
Fig.  4.     Distribution  of  improvement  in  the  preliminary  tests  by  age  and 
sex,  417  boys  and  490  girls. 


EFFECT  OF  TRAINING  IN  PITCH  DISCRIMINATION         73 

The  efifect  of  the  instruction  and  experience  thus  gained  from  the 
first  to  the  second  test  is  shown  in  Fig.  2  which  represents  only  the 
46  per  cent,  of  cases  in  which  improvement  was  made.  Fig.  3 
shows  the  efifect  upon  the  whole  group  of  1980  cases.  Fig.  4  shows 
the  distribution  of  improvement  by  age  and  sex. 

TABLE  II.    Distribution  of  forty-seven  out  of  fifty-four  university  students 
who  improved  with  individual  instruction 


^3 

17 

12 

8 

5 

3 

A 

B 

30 

I 

I 

I 

2 

I 

0 

6 

17 

12 

8 

5 

3 

2 

^3 

0 

0 

I 

I 

0 

0 

2 

I 

12 

8 

5 

3 

2 

I 

17 

0 

0 

4 

I 

2 

8 

I 

8 

5 

3 

2 

/ 

0.5 

12 

2 

2 

I 

0 

2 

8 

I 

5 

3 

2 

0.5 

8 

3 
3 

6 
2 

2 
I 

0.5 

0 

12 

5 

5 

4 

I 

4 

2 

II 

II 

Below  5 

28 

Notation  and  pi 

an  of  this 

table 

same  as  in 

Table  I. 

A  similar  test  of  the  efifect  of  instruction  was  made  in  a  class  of 
200  adults.  After  two  preliminary  tests,  one  heterogeneous  and  one 
homogeneous,  the  poorest  one-fourth  of  the  group  were  taken  and 
instructed  individually  as  to  the  actual  nature  of  pitch  hearing.  An 
effort  was  made  to  find  out  what  particular  difficulties  they  were 
encountering,  and  explanation  and  illustration  were  based  progress- 
ively upon  this  information.  As  a  class  these  had  made  but  little 
improvement  in  the  second  preliminary  test,  both  the  first  and  the 
second  having  been  given  "without  i'nstruction".  But  as  a  result 
of  this  personal  instruction  all  but  7,  i.e.  47  out  of  the  54  made 
rapid  improvement.  The  change  in  the  record  for  the  group  is 
shown  in  Fig.  5  by  giving  the  distribution  at  the  begiYining  and  at 
the  end  of  the  period  of  individual  instruction.  The  distribution 
of  the  gain  is  analyzed  in  Table  II. 

The  fact  that  these  were  adults  familiar  with  the  class  room  and 
trained  in  many  psychological  experiments,  yet  made  such  marked 
response  to  the  instruction  and  individual  help,  doubly  emphasizes 
the  i'mportance  of  thoroughness  and  individual  attention  in  the  in- 
structions if  the  records  are  to  be  entirely  reliable. 

One  of  the  best  experimental  proofs  that  we  have  showing  the 
efficacy   of   individual   care   and   instruction   is    found   in   the   un- 


74 


FRANKLIN  O.  SMITH 


Second  fej* 


Fig.  5.     Distribution  of  54  university  students  in  individual  tests  (Table  11). 


published  experiments  of  Dr.  H.  S.  Bufifum,  which  have  been  sum- 
marized in  the  above  mentioned  Psychological  Association  report 
by  Professor  Seashore,  as  follows: 

Dr.  Buffum  experimented  on  twenty-five  eighth  grade  pupils  in  a 
grammar  school  room.  He  first  made  a  fifteen  minute  individual 
test  of  each  pupil  and  classified  them  on  this  basis  into  three  groups 
with  modes  at  3,  8  and  17  v.d.  respectively.  The  object  was  two- 
fold :  (i )  to  determine  the  effect  of  practi'ce  and  (2)  to  determine  the 
success  of  the  preliminary  examination.  For  this  purpose  he  gave 
them  twenty  forty-five-minute  periods  of  training. 

The  results  show  (i)  that  for  no  group  is  there  any  evidence  of 
improvement  with  this  practice,  and  (2)  that  all  except  two  chil- 
dren remained  throughout  the  whole  practice  series  within  the. 
group  to  which  they  had  been  assigned.  Of  these  two,  one  who 
had  been  assigned  to  group  III  was  immediately  found  to  belong 
to  group  I  as  there  had  been  a  failure  to  understand  the  pre- 
liminary test;  and  the  other,  although  retained  in  group  II,  proved 
really  to  be  near  the  dividing  line  and  could  have  been  classified  in 
group  III.  Evi'dently  the  physiological  threshold  had  been  reached 
in  twenty-four  of  the  twenty-five  cases  in  the  preliminary  test." 

In  Dr.  Buflfum's  experiment  the  fifteen-minute  preliminary 
classification  was  so  efficient  as  practically  to  eliminate  poor  records 
due  to  ignorance  of  the  test. 

The  significance  of  instruction  is  further  proved  by  the  records 
in  successive  classes  in  the  university  for  a  period  of  years.  It  is 
found  that  the  average  record  has  improved  slightly  from  year  to 
year.     There  is  no  reason  for  believing  that  this  is  due  to  anything 


EFFECT  OF  TRAINING  IN  PITCH  DISCRIMINATION         75 

but  improved  skill  and  technique  and  increased  care  in  the  instruc- 
tions and  charge  to  those  about  to  be  examined. 

In  the  above  records  we  have  conclusive  evidence  that  effective 
instruction  is  of  the  greatest  importance  in  making  records  on  pitch 
discrimination.  It  is  not  a  poor  ear,  but  ignorance  that  accounts  for 
the  bulk  of  poor  records  in  a  first  test.  Those  who  made  a  fine 
record  in  the  first  test  are,  of  course,  not  subject  to  this  source  of 
error;  and  those  who  have  poor  records  but  show  no  improvement 
after  instruction  or  prolonged  training  may  also  be  free  from  this 
source  of  error.  It  is  a  safe  rule  to  say  that  all  tests  should  be  pre- 
ceded by  efficient  instruction ;  if  this  can  be  made  individual,  so  much 
the  better;  and  all  who  show  poor  records  must  be  subjected  to 
more  intensive  and  searching  instruction  before  the  record  can  be 
accepted  for  serious  purposes. 

The  effect  of  practice 

The  first  of  the  two  extensive  experiments  in  practice  was  a 
series  of  group  tests  by  the  "heterogeneous"  method  covering  a  period 
of  ten  days.  The  second  was  a  series  of  individual  tests  on  adults 
by  the  "homogeneous"  method.  In  addition  to  these  certain  special 
training  series  will  be  described. 

The  group  tests  were  made  on  476  pupils  (215  boys  and  261  girls) 
in  two  elementary  schools  selected  from  those  in  which  the  pre- 
liminary tests  had  been  made.  These  practi'ce  tests  were  conducted 
in  the  same  manner  and  under  the  same  conditions  as  the  prelimin- 
ary tests  except  with  regard  to  instruction.  Each  test  was  preceded 
by  a  brief  warming-up  exercise  in  which  the  pupils  answered  orally. 
This  also  helped  to  keep  interest  alive.  A  short  rest  period  was 
taken  at  the  middle  of  each  test.  At  this  time  opportunity  was 
given  the  pupils  to  ask  questions  about  the  test. 

Running  parallel  with  the  class  tests  were  certain  individual  tests 
which  were  carried  on  in  the  afternoon  foUowi'ng  a  given  set  of  class 
tests.  At  the  noon  intermission  the  records  of  one  or  two  grades 
were  checked  up  and  pupils  whose  threshold  for  that  day  was  be- 
tween 20  v.d.  and  30  v.d.  were  given  individual  practice.  The 
object  of  these  individual  tests  was  to  give  special  assistance  to 
backward  pupils,  aiding  them  to  distinguish  different  tone  qualities 
and  to  form  right  habits  of  attention.  These  tests  include  71  boys 
and  35  girls  constituting  the  poorest  in  the  group  tests. 


76 


FRANKLIN  O.  SMITH 


With  regartl  to  the  general  musical  preparation  of  these  pupils 
it  may  be  said  that  music  was  taught  systematically  in  all  the  grades, 
and  that  the  schools  were  provided  with  Victor  graphophones  in 
which  high  grade  selections  were  played  regularly. 

For  comparison  the  cases  under  observation  may  be  divided  as 
follows :  Group  I,  those  who  made  no  improvement  either  with 
instruction  or  practice ;  Group  II,  those  who  made  no  improvement 
in  the  practice;  Group  III,  those  who  made  little  (1-3  v.d.)  improve- 
ment in  the  practice;  and  Group  IV,  those  who  made  marked  im- 
provement (3  v.d.  +)• 

The  records  of  these  practice  series  on  children  are  set  forth  in 
Tables  III-IX  and  Figs.  6-10.  Table  III  gives  the  daily  average 
threshold  for  the  twelve  days  of  training  by  ages,  section  A  showing 
those  who  do  not  improve  with  training  and  B  those  who  do  im- 
prove with  training.  Table  IV  gives  the  daily  average  threshold  for 
those  who  improve  with  training  regardless  of  age  for  the  four 


Fig.  6.     Daily  average,  by  groups,  of  those  in  the  practice  series  (Table  VI). 


.3c 


oj/a 


_J_Lj_i__ 

:r-u:i:u' 

aj/s  Z        3        1        S       6 


•+'--1 


Fig.  7.     Daily  average  by  sex   (Table  V). 


EFFECT  OF   TRAINING  IN  PITCH  DISCRIMINATION 


77 


Fig.  8. 


QS    '~i         2         5         J         a        11        Tj        73       30       Jor 
Distribution  of  270  pupils  who  improved  with  practice  (Table  VI). 


Fig.  9.     Daily  average  record  of  those  who  were  given  special  individual 
help    (Table  VII). 


'->-s.. 


.....CHrfe 


'3        If        15        16        17  '/6       le^ 

Comparison  by  ages  of  the  average    (median)    abilities  of  boys 


Fig.   10. 
and  girls. 

groups.  Table  V  gives  the  averages  of  the  same  separately  for  the 
boys  and  girls,  Groups  II,  III,  and  IV  combined.  Table  VI  gives  an 
analysis  of  the  distribution  of  those  who  improve  with  practice.  Ta- 
ble VII  (Fig.  9)  contains  the  record  of  those  who  were  given  indi- 
vidual tests  or  help  during  the  practice,  showing  the  daily  record  and 
the  record  of  two  individual  tests  in  the  average  for  the  group.  Table 
VIII  gives  a  compari'son  of  the  mean  variations  with  reference  to  sex 
and  age.  Table  IX  gives  the  distribution  of  those  who  attain  the 
approximate  physiological  threshold  in  different  days  of  the  practice. 


FRANKLIN  O.  SMITH 

TABLE  III.    Daily  average  threshold,  by  age 
A.     Group  I :  those  who  made  no  improvement  with  training 


Age 

J 

2 

3 

4 

5 

6 

7 

8 

9 

10 

II 

12  : 

Number 

9 

6 

6 

6 

6 

8 

7 

8 

10 

9 

8 

7 

8 

29 

lO 

6 

6 

4 

7 

8 

8 

6 

7 

7 

8 

6 

8 

31 

II 

8 

4 

6 

7 

5 

7 

6 

7 

5 

6 

7 

8 

47 

12 

8 

8 

8 

5 

7 

8 

7 

7 

8 

8 

8 

5 

23 

13 

5 

5 

5 

5 

4 

5 

5 

5 

4 

4 

5 

5 

29 

14 

6 

5 

5 

5 

4 

4 

5 

4 

4 

4 

4 

5 

32 

15 

5 

6 

5 

5 

4 

4 

4 

4 

4 

4 

4 

4 

15 

B. 

Gro\ 

ups 

//,  ///, 

,  IV 

comb 

ined: 

f/;oj^  w/; 

0  made 

impro 

t'^m^nf 

Age 

I 

2 

3 

4 

5 

6 

7 

8 

9 

10 

II 

12 

Number 

9 

7 

5 

5 

5 

4 

4 

4 

4 

4 

3 

3 

2 

16 

10 

7 

7 

5 

5 

4 

4 

5 

3 

3 

3 

3 

3 

43 

II 

10 

10 

8 

7 

8 

5 

5 

5 

6 

5 

4 

5 

43 

12 

7 

5 

4 

3 

3 

3 

2 

2 

2 

2 

2 

2 

53 

13 

8 

8 

5 

5 

6 

4 

4 

4 

3 

2 

2 

2 

51 

14 

7 

7 

5 

s 

5 

5 

4 

3 

4 

3 

3 

3 

34 

15          787555433343  30 

Ave.           7.5     7-1      5-7     5-0     5-0     4-3     4-1      3-4     3-5     3-0  3.0     2.9 

%  gain               9      30      15        o      15        4       I5        o        9  o        2 

TABLE  IV.    Daily  average  by  groups 

I       23456789      10  II 

Group  I            5-9    4-8     5-2     5-8    5-i     5-5     5-4    S-O    5-4    5-2  5-1 

Group  II           8.5     9-0    3-3    4-6    7-6    5-3     4-7    4-0    4-0    3-5  3-0    5-0 

Group  III         6.9    6.2     5.4     5-1     5-0    5-8    4-5     3-5     3-5     3-4  3-1 

Group  IV        15.0  lo.o    8.2     5.5     5-1     5-i     3-i     3-4    2.5     2.9  2.6 

TABLE  V.     (Fig.  7)  Daily  average  by  sex  for  Groups  II,  III.  and  IV 

Number          i       2       3       4       5       6       7       8  9      10      n      12 

Boys.                 215            8.1     6.5     6.3     5.8     5-6     5-2    5-3     5-2  5.0    4-6    4-6    4-7 

Girls:                261            6.3     5-3     5-2     5-2    4-9    4-8    4-7    4-7  4-5     4-0    3-5    4-5 


12 

Number 

5-4 

206 

5-0 

52 

30 

172 

2.7 

46 

TABLE  VI.    Distribution  of  those  who  improve  with  practice 


30+ 
30 
23 
17 


30 

23 

17 

12 

5 

5 

i? 

2 

/ 

0-5 

0 

I 

I 

2 

2 

I 

0 

0 

I 

0 

23 

// 

12 

8 

5 

3 

2 

I 

0.5 

3 

2 

4 

I 

2 

I 

I 

0 

17 

12 

8 

5 

J 

2 

/ 

0.5 

4 

5 

4 

4 

2 

I 

I 

0 

12 

5 

5 

3 

-? 

/ 

0.5 

5 

7 

3 

2 

I 

0 

0 

,S* 

5 

? 

2 

/ 

0.5 

8 

10 

8 

3 

I 

I 

5 

3 

2 

I 

0.5 

14 

26 

15 

6 

6 

3 

2 

/ 

0.5 

15 

26 

10 

4 

2 

/ 

0.5 

12 

16 

14 

I 

0.5 

4 

8 

18  8 

31  14 

67  25 

53  33 

42  55 

12  59 

Below  2  73 
Notation  and  plan  of  this  table  same  as  in  Table  T. 


EFFECT  OF  TRAINING  IN  PITCH  DISCRIMINATION        79 


TABLE  VII.    Daily  average  record  of  those  who  were  given  special 

individual  help 

Days            12        34 

5678        9       10       II      12 

Boys:          17.3  12.     12.5  12.5 

14.5  15.5  12.5  114  1 1-3  1 1.2    9-5    9-8     12.        8. 

Girls            17.7  11.8    9.5  11.5 

1 1.4  10.5  10.5    8.      8.5    8.4    7-9    7-8      8.2      5.3 

Italics,   average   record   on 

the   first   and   the   second   individual   tests   re- 

spectively 

TABLE  VIII.    Average  mean  variation  from  the  individual  records  in  the 

preliminary  and  final  tests. 

Boys  (215) 

Girls  (261) 

Age      Prelim. 

Final                     Prelim.             Final 

9                1.82 

1.93                            1.99                1-97 

10                1.66 

1.81                            1.76                1.60 

II                1.63 

1. 7 1                            1.68                1.82 

12                1.70 

1.53                           1-51                1-68 

13                147 

1.52                          I.S4               i-6o 

14                145 

1.48                          1. 6s               1.65 

15                1.64 

1.59                         1.53               1-38 

Total          1.61 

1.65                          1.65               1.69 

TABLE  IX.    Distribution  of  those  who  reach  the  approximate  physiological 

threshold  ( 

on  different  days  of  practice. 

Days            I            2            3 

4            5            6            7            8            9          10 

Per  cent.    689 

9            9          13          12          13            8            7 

Of  the  476  children  206  (43%)  fall  in  Group  I;  i.e.,  so  far  as 
the  instruction  and  practice  are  concerned,  these  made  no  improve- 
ment that  could  be  traced  in  the  records,  due  allowance  being  made 
far  daily  variable  errors.  The  number  of  those  who  do  not  improve 
with  practice  is  relatively  greater  for  the  younger  than  for  the 
older  children. 

Classifying  these  260  on  the  basis  of  record  into  Grade  A,  those 
whose  threshold  is  4  v.d.  or  less ;  Grade  B,  those  whose  threshold 
is  between  4  v.d.  and  14  v.d. ;  and  Grade  C,  those  whose  threshold 
lies  above  14  v.d.,  we  find  40  per  cent,  in  Grade  A,  51  per  cent,  in 
Grade  B,  and  9  per  cent,  in  Grade  C.  Of  the  270  cases  (57  per 
cent.)  which  show  improvement  with  practice  19  per  cent,  are  in 
Grade  A,  64  per  cent,  in  Grade  B  and  17  per  cent,  in  Grade  C. 

Relatively  the  largest  number  of  cases  of  improvement  occur 
among  those  who  start  out  with  a  very  inferior  record.  This  can  be 
shown  by  comparing  the  distribution  of  cases  which  make  improve- 
ment for  each  of  the  increments  as  set  out  in  Column  A,  Table  VI 
with  the  normal  distribution  of  thresholds  for  the  entire  group. 

Of  those  who  did  not  improve  ten  were  unable  to  hear  any  of  the 
increments  used  and  judge  as  required.    It  was  however  found  upon 


8o  FRANKLIN  O.  SMITH 

making  private  examination  of  the  seven  of  these  who  were  avail- 
able that  they  could  hear  tone  differences.  Two  of  these  could  distin- 
guish between  A  and  B  on  the  piano.  Two  of  them  seemed  unable 
to  grasp  the  concepts  "high"  and  "low"  with  reference  to  the 
naming  of  pitch.  One  of  these — a  scatter-brain — could,  however, 
sing  a  half-tone  correctly  when  played  on  the  piano.  The  other — re- 
tarded about  five  years — could  sing  a  fifth  fairly  accurately  with  the 
piano.  Three  were  able  to  imitate  a  pitch  difference  in  the  forks  of  3 
v.d.  by  singing  enough  to  show  whether  the  second  of  the  two  tones 
was  sharp  or  flat.  The  other  three  were,  unfortunately,  not  avail- 
able for  special  tests.  Thus,  of  the  476  cases  not  a  single  case  of 
so-called  tone  deafness  was  found. 

The  last  line  in  the  footings  of  Table  III,  B  shows  that  the  gain 
of  those  who  do  improve  is  most  rapid  in  the  first  part  of  the  train- 
ing series,  54  per  cent,  of  the  gain  being  made  in  the  first  three 
steps.  The  further  analysis  of  these  figures  in  Table  IV,  illustrated 
by  Fig.  6,  shows  that  this  principle  is  true  for  all  three  of  the  groups 
which  show  improvement. 

All  the  observers  included  in  Table  VII  took  the  first  individual 
test  which  occurred  on  different  days,  from  the  third  to  the  seventh 
day.  Most  of  these  tests  were  given  early  in  the  practice  series.  The 
second  test  began  on  the  fifth  day  and  extended  over  the  remainder 
of  the  practice  series.  Only  26  boys  and  9  girls  needed  to  take  this 
test.  A  very  few  were  given  a  third  test  near  the  end  of  the  prac- 
tice but  the  results  were  not  included  in  the  table.  Not  only  does 
the  individual  test  yield  a  lower  median  than  the  group  test  in  a 
majority  of  cases,  but  the  individual  test  often  influences  the  later 
results  of  group  practice.  In  this  experiment  6  boys  and  4  girls 
made  immediate  and  permanent  improvement  after  the  first  individ- 
ual test  which  it  will  be  remembered  was  accompanied  by  instruc- 
tion. In  one  case  the  gain  was  from  30  to  9  v.d. ;  in  another  from 
23  to  5  v.d.  and  in  a  third  from  24  to  10  v.d.  In  some  cases  im- 
provement did  not  begin  until  after  the  second  test,  and  in  the  case 
of  29  boys  and  13  girls  no  improvement  was  made.  Of  these  only 
2  (both  girls)  made  better  records  in  the  individual  tests. 

The  average  amount  of  improvement  for  all  cases  at  each  incre- 
ment decreases  with  the  diminishing  of  the  increment.  This  is  seen 
in  Table  VI,  and  may  also  be  seen  graphically  in  Fig.  8.  It  must  be 
remembered  that  this  figure  does  not  represent  the  whole  group 
but  only  those  who  improved. 


EFFECT  OF   TRAINING  IN  PITCH  DISCRIMINATION         8i 

The  series  is  not  long  enough  to  guarantee  that  any  or  all  reached 
the  physiological  threshold.^  The  main  difficulty  in  determining 
this  lies  in  the  fact  that  persons  often  come  to  a  "plateau"  in  the 
record  which  is  due  to  some  motive  or  condition  which  may  be  re- 
moved by  instruction  or  training.  This,  however,  gives  trouble  only 
when  it  continues  to  the  end  of  the  training  series.  Classifymg  the 
cases  roughly  on  internal  evidences  of  the  records  we  find  that  what 
may  be  approximately  the  physiological  limit  is  reached  in  successive 
days  as  set  forth  in  Table  IX.  From  the  variations  in  the  records 
it  is  quite  clear  that  the  data  in  this  table  are  quite  problematical. 
To  get  the  actual  physiological  threshold  it  is  necessary  to  have  more 
favorable  conditions  for  isolation  of  the  observer  and  the  elimina- 
tion of  disturbances.  Undoubtedly  there  may  also  be  several  who 
remain  on  a  "cognitive"  plateau  throughout  this  series  and  would 
improve  under  the  proper  impetus.  Yet,  due  allowance  being  made 
for  these  sources  of  error,  the  table  shows  that  there  is  a  "rapid 
maturing"  in  this  training ;  6  per  cent,  reach  their  bed-rock  level  on 
the  first  day,  8  per  cent,  on  the  second,  9  per  cent,  on  the  third,  etc. 

After  the  preliminary  tests  the  number  who  reach  the  approxi- 
mate physiological  threshold  increases  gradually  to  the  fourth  day. 
On  the  fifth  day  the  number  increases  suddenly  from  24  to  41  (9 
per  cent,  to  15  per  cent.)  and  then  gradually  decreases  to  the  eighth 
day  after  which  there  is  a  rapid  falling  off  to  the  tenth  day.  (Table 
IX.)  The  results  show  that  47  per  cent,  of  those  who  improve 
reach  the  approximate  physiological  threshold  by  the  fifth  day  of 
practice. 

The  mean  variation  as  given  in  Table  VIII  conveys  the  signi- 
ficant items — the  result  of  practice,  the  variations  with  age,  and  the 

"The  term  is  here  used  in  the  sense  defined  by  Seashore  (3)  page  49-SO. 
"The  Cognitive  vs.  the  Physiological  Threshold.  In  sensory  discrimination 
of  this  sort  we  may  speak  of  two  thresholds:  the  physiological,  which  is 
set  by  the  Hmits  of  capacity  in  the  end  organ;  and  the  cognitive,  which  is 
set  by  cognitive  limitations.  Theoretically  we  always  aim  to  reach  the  physio- 
logical threshold,  but  practically  we  often  fall  short  of  this  and  find  a  cog- 
nitive limit;  i.e.,  a  higher  threshold  due  to  lack  of  information,  best  form 
of  attention,  interest,  effort,  etc.;  or  to  disturbances  of  some  sort.  Usually 
inspection  of  a  record  or  observations  made  in  the  test  enable  us  to  tell 
whether  or  not  we  have  reached  the  physiological  threshold.  It  cannot  be 
judged  by  a  single  rule,  although  a  small  m.v.  and  a  well  defined  mode 
are  pretty  sure  indications.  This  distinction  is  of  greatest  importance  in 
classification,  and  in  the  theory  of  training." 


82  FRANKLIN  O.  SMITH 

variations  with  sex.  It  must  be  borne  in  mind  that  the  unit  of  the 
m.v.  is  not  the  vibration  but  the  increment,  as  was  described  above. 
That  is,  the  increments  increase  in  a  geometric  ratio  of  the  second 
order;  therefore,  e.g.,  the  increment  17-23  v.d.  counts  one  unit  just 
as  do  the  increments  5-8  v.d.  or  1-2  v.d.  It  follows  that  as  the 
threshold  is  lowered  the  mean  variation  unit  remains  relatively 
constant.  Equal  power  of  application  of  those  who  have  high  and 
those  who  have  low  thresholds  should  therefore  show  in  about 
equal  mean  variations;  and,  conversely,  unreliability  in  judgment 
wall  show  in  increased  mean  variation  equally  for  the  one  who  has  a 
fine  ear  and  the  one  who  has  a  poor  ear. 

The  mean  variation  is  slightly  larger  in  the  final  training  test  than 
in  the  preliminary.  The  difference  is  not  large— only  .04  units — 
but  it  is  fairly  constant  for  all  ages  and  for  both  sexes.  This  is 
rather  remarkable  as,  in  the  nature  of  the  test,  one  would  look  for 
evidences  of  increasing  familiarity  in  the  lowering  of  the  mean 
variation.  On  the  other  hand  the  fact  that  the  procedure  does  not 
reduce  the  mean  variation  is  a  most  telling  proof  of  the  elemental 
nature  of  the  test.  The  test  is  so  stripped  of  conditions  for  varia- 
bility that  it  is  possible  to  be  as  consistent  in  the  preliminary  trial  as 
in  trials  after  practice. 

The  variability  is  a  trifle  larger  for  girls,  both  in  the  preliminary 
and  the  final  tests.  This  is  true  for  all  the  ages  except  12  and  15 
in  the  preliminary  and  10  and  15  in  the  final.  Were  it  not  that  this 
has  a  bearing  on  the  much  mooted  question  of  sex  difference  on  this 
point  and  that  the  data  here  given  represent  such  a  large  number 
of  cases  (1980  in  the  preliminary  and  476  in  the  final)  no  signifi- 
cance would  be  attached  to  this  difference.  The  second  decimal 
figure  is  of  doubtful  value  in  an  average  of  this  kind  and,  as  stated, 
the  variation  is  in  one  direction  for  five  ages  and  in  the  opposite 
for  two  both  in  the  preliminary  and  the  final.  On  the  whole  our  in- 
terpretation is,  therefore,  that  practically  there  is  no  significant 
difference  in  the  variability  of  the  boys  and  the  girls  in  pitch 
discrimination. 

There  is  a  general,  though  not  great,  tendency  for  the  mean 
variation  to  decrease  with  age.  This  is  the  measure  of  growing 
reliability  with  age  which  we  are  accustomed  to  find  in  records  of 
this  kind. 

In  this  practice  series  in  the  elementary  schools  there  are  two 


EFFECT  OF   TRAINING  IN  PITCH  DISCRIMINATION 


83 


items  that  count  distinctly  in  favor  of  the  girls.  One  is  that  of  the 
215  boys  and  261  girls  who  took  the  practice  series,  71  boys  and  35 
girls  were  considered,  on  the  same  basis,  poor  enough  to  need  in- 
dividual instruction  and  drill.  This  is  a  distinct  mark  of  superiority 
in  the  girls.  The  other  is  that  the  girls  in  the  training  series,  quite 
uniformly  for  all  ages,  have  a  lower  threshold  than  the  boys  by 
from  one  to  two  vibrations.     (See  Table  V,  and  Fig.  7). 

This  superiority  of  the  girls  over  the  boys  is  evidenced  also  in  the 
preliminary  tests  with  remarkable  uniformity  as  is  seen  in  Fig.  10 
where  a  fairly  constant  difference  is  maintained  throughout  all  the 
ages.  The  same  fact  is  illustrated  from  another  point  of  view  for 
the  elementary  school  in  Table  X  and  Fig.  11.  This  difference, 
however,  disappears  when  we  come  to  the  higher  ages.  Fig  12,  for 
the  high  school,  and  Fig.  13  for  the  university,  based  on  Table  X 
reveal  no  recognizable  superiority  of  either  sex  in  the  preliminary 
tests. 

— fi. 


-     .-.-i-r  t  -i~r  ->•••?  -I 

^  _/     ZJ<Sfli2l7Z3X30t  Cd 


s  a  iz  17  g3  30  J0f^d3~t    a  3  ^  e  iz  n  zjko 


Figs.  II,  12,  13.     Variation  with  sex  and  age. 
in  tlie  elementary  schools. 


Based  on  preliminary  tests 


A  comparison  of  pitch  discrimination  for  different  ages  in  the 
preliminary  tests  is  given  in  Table  X.  This  shows  that  the  order  of 
superiority  is, — university  students,  high  school  pupils,  and  elemen- 
tary pupils,  the  respective  modes  being  roughly  2,  3,  and  4  v.d.  This 
comparison  is  however  not  quite  fair,  inasmuch  as  longer  tests  were 
given  to  the  university  students  than  to  the  high  school  pupils  and 
longer  to  the  high  school  pupils  than  to  the  elementary  pupils ;  and 
the  longer  the  test  the  more  favorable  the  results  tend  to  be.  As 
will  be  shown  later,  this,  together  with  the  better  control  of  experi- 
mental condition  among  the  older  pupils,  may  be  ample  to  account 
for  the  differences  here  shown,  so  that,  under  equally  good  condi- 
tions of  testing,  there  would  probably  be  no  evidence  of  variation 
with  age. 

In  Table  XI  we  see  that  at  the  age  9  the  cases  are  about 
equally  distributed  in  the  three  grades.     Grade  B  remains  about 


84 


FRANKLIN  O.  SMITH 


constant  for  all  ages ;  but  the  number  of  cases  in  Grade  A  decreases 
with  age  as  the  number  of  cases  in  Grade  C  increases.  Fig.  14 
shows  a  comparison  for  age  only. 


-/Y\ 


Fig. 
ages. 


z        3        J       5^    72       77       TT     30      30t 
Comparison   of   threshold   of   pitch    discrimination    for    different 


TABLE  X   (Fig.  11,  12,  13  and  14).     Variation  with  age  and  sex 


Grade 
C 


Grade 
B 


Grade 
A 


(Preliminary  tests). 

Elementary  School 

High  School 

University 

.d. 

M 

F 

M 

F 

M        F 

30+ 

8 

5 

3 

3 

0         0 

30 

5 

3 

2 

I 

I          0 

23 

5 

2 

3 

2 

2          I 

17 

8 

6 

2 

2 

3           4 

12 

8 

6 

6 

5 

3          5 

8 

17 

20 

12 

14 

9        II 

5 

17 

19 

21 

20 

13         II 

3 

18 

22 

26 

34 

22         25 

2 

8 

10 

14 

13 

26        32 

I 

5 

6 

10 

5 

14         ID 

V2 

0 

I 

I 

I 

7          I 

Af  males;  F  females;  numbers  indicate  the  per  cent,  of  cases  at  each  step. 
A  4  v.d.  or  less ;  B  between  4  v.d.  and  14  v.d. ;  C  above  14  v.d. 


TABLE  XI.  Distribution  by  age  and  group  in  terms  of  per  cent,  of  cases 

Age  9  10        II         12        13         14        15         16        17        18        19-f- 

Group  A     30  24        24        16        17        12        13         12  8  4  8 

Group  B     38  44        40        44        41        44        40        34        34        47        36 

Group  C     32  32        36        40        42        44        47        54        58        49        66 


The  comparison  of  the  mean  variation  for  the  three  groups  of 
ages  given  in  Fig.  15  shows  that  the  rehability  of  the  records  of 


EFFECT  OF   TRAINING  IN  PITCH  DISCRIMINATION 


85 


the  high  school  pupils  is  practically  as  good  as  that  of  university 
students.  Elementary  pupils  are  slightly  inferior  but  not  so  much 
as  we  would  ordinarily  find  in  other  tests  of  discrimination. 


t 


'-h 


16 

IZ 
10 
8 
6 
<? 
Z 


;  1/   !\  \  Elementary  eahool 

'/ \-.f.^ ^'3^  SehooJ 


--Vs. 


2^ 


.^     6   .8    10    l£   /^    16    L8  20  2.2  Zff  Z6  2B  dO         S'f 
Fig.    15.     Comparison   of   mean  variation    (m.v.)    in  the  preliminary  tests 
for  different  ages. 

Some  records  of  practice  in  pitch  discrimination  have  been  col- 
lected incidentally  in  this  laboratory.  The  case  of  C.E.S.  is  pre- 
sented (Fig.  16)  to  illustrate  how  variable  the  threshold  may  be 
aside  from  practice.  The  first  practice  series  of  twenty  half-hour 
periods  was  taken  in  1898  with  crude  methods.  No  resonator  was 
used,  the  forks  being  held  to  the  ear.  This,  perhaps,  introduces  the 
largest  source  of  error  in  that  series.  Unfortunately  data  are  not 
available  for  determining  other  causes  of  the  inferiority  of  this 
record.  Beginning  with  1906  the  Koenig  resonators  were  used  with 
a  good  quality  of  forks.  The  fact  that,  from  this  point  on,  the 
record  is  fairly  constant  would  seem  to  indicate  that  the  absence  of 
the  resonator  in  the  foregoing  series  was  the  chief  source  of  error. 
In  1907  the  experimenter  was  not  skilled.  In  1910  the  tests  were 
made  for  the  purpose  of  comparing  certain  conditions  of  environ- 
ment, such  as  the  light  and  sound-proof  room,  a  class  room,  and  out 
in  the  open  air.  From  the  43rd  to  the  48th  day  a  study  was  made 
of  the  efifect  of  the  duration  of  the  tone  and  the  time  interval  be- 
tween the  two  tones.  On  the  last  four  days  distractions  were  intro- 
duced. The  best  record  was  made  while  the  observer  was  intention- 
ally tracing  a  maze. 


86 


FRANKLIN  O.  SMITH 


Something  was  wrong  in  1898.  M.  C.  W.  (Fig.  17)  made  a  poor 
record  in  the  twenty  period  practice  undertaken  by  the  same  method 
and  means  as  in  the  case  of  C.  E.  S.  above.  In  1908,  as  soon  as  the 
good  resonator  was  introduced,  her  record  was  fine  and  free  from 
fluctuations.  She  had,  however,  learned  to  play  the  violin  and  had 
gained  experience  in  the  tuning  of  forks  in  the  years  that  elapsed 
since  1898.  Her  best  records  ware  made  with  distractions — tracing 
a  maze  or  crocheting.  These  records  furnish  most  striking  evidence 
of  the  importance  of  reliable  apparatus  and  technique. 

In  Fig.  18,  characteristic  results  of  practice,  under  most  favorable 
conditions  of  control  are  shown;  a,  b,  c,  and  d  are  the  respective 
practice  curves  for  four  graduate  students  practicing  one  hour  daily, 
sixteen  days. 


SbjiJ     J  /O  15  zo 

P'ig.  16.     Record  of  C.  E.  S. 


£5  30  35  fO 


«■  50  St 


zo  Z5  Z9 


Fig.  17.     Record  of  M.  C.  W. 


1  I  I  --^  i\'/\iy'/' \i  »  ' 


%j2     3    9    5    6     7 
Fig.  18.     The  effect  of  training. 


I      I      I      I      I      '      I      ' 
8    9    10   II    IZ    13    A*    '5 


EFFECT  OF   TRAINING  IN  PITCH  DISCRIMINATION         87 

Factors  in  the  development  of  pitch  discrimination 

Practice  in  pitch  discrimination  means  (i)  the  control  of  a 
special  set  of  cognitive  factors  involved  in  learning  to  recognize 
differences  in  pitch,  and  (2)  the  acquisition  of  skill  in  listening  to 
musical  tones.  In  most  of  the  recent  experiments  on  practice,  such 
as  those  made  by  Book  on  typewriting,  Swift  on  tossing  balls, 
Bryan  and  Harter  on  telegraphy,  Judd  and  others  on  handwriting, 
and  Huey  on  reading,  the  object  has  been  to  determine  the  mode 
of  acquisition  of  certain  special  habits.  Of  these  Book  distinguishes 
two  sorts,  habits  of  manipulation  and  habits  of  control ;  The  latter 
he  defines  as  certain  general  or  more  purely  psychic  habits  ac- 
quired in  the  course  of  practice.  It  is  to  this  type  of  learning  that 
the  OKsent  analysis  is  directed.  Of  these  general  habits  or  modes 
of  control  we  may  distinguish  three  types,  (i)  sensory  control,  by 
which  is  meant  acquaintance  with  certain  sensational  facts,  such  as 
auditory  qualities  of  the  tones,  and  muscular  sensations;  (2)  as- 
sociational  control,  or  acquaintance  with  memory  images,  as  audi- 
tory, visual,  and  motor;  and  (3)  control  of  special  attitudes,  as  feel- 
ing of  familiarity,  most  favorable  form  of  attention,  interest,  etc. 

Auditory  and  kinaesthetic  sensations  seem  to  play  the  leading  role 
in  judging  differences  in  pitch.  Two  types  of  observers  may  be 
distinguished.  First,  there  are  those  whose  perception  of  pitch  is 
chiefly  in  terms  of  tonal  qualities.  They  learn  to  direct  attention 
to  the  characteristic  sharpness  or  fineness  of  the  high  tones  and  to  the 
flatness  or  dullness  of  the  low  tones.  The  particular  sensory  quality 
of  the  tone  varies  with  different  persons.  One  notices  that  the 
high  tone  is  sharper,  and  has  a  tendency  to  last  longer  in  the 
ear  than  the  low  tone.  Another  describes  the  high  tone  as  finer 
and  more  piercing.  The  lower  tone  is  usually  distinguished  from 
the  higher  as  being  duller,  deeper,  heavier,  and  more  mellow. 
It  is  also  interesting  to  note  that  some  observers  judge  altogether 
by  the  high  tone,  while  others  judge  only  by  the  low  tone.  Some 
persons  seem  to  have  an  affective  preference  for  high  tones,  others 
for  low  tones.    This  forms  an  apperceptive  basis  for  the  judgment. 

Second,  there  is  a  considerable  number  who  depend  largely  upon 
kinaesthetic  sensations  of  the  vocal  organs  in  making  the  judg- 
ment. Regarding  these  Stumpf  says:  "If  the  muscular  sense  in 
the  vocal  organs  is  the  same  as  a  former  tone  that  we  have  heard, 
we  judge  that  it  is  the  same  tone.     If  we  are  told  that  a  certain 


88  FRANKLIN  O.  SMITH 

tone  is  A,  we  remember  that  a  tone  giving  the  same  sensations 
is  A.  If  the  muscular  sense  changes  in  a  definite  way  when  we 
sing  two  tones,  we  say  that  the  tones  rise.  If  a  distance  is  notice- 
able in  the  change,  we  judge  the  second  interval  to  be  greater." 
Strieker  did  not  think  of  music  in  terms  of  notes  nor  of  auditory 
images,  but  in  terms  of  muscular  sensations  in  the  vocal  cords.  He 
speaks  of  the  impossibility  of  the  reproduction  of  a  tone  in  the  mem- 
ory without  bringing  into  play  the  actual  or  intended  use  of  the  vocal 
organs.  He  considers  the  connection  between  tone  perception  and 
the  innervation  of  the  vocal  organs  a  sort  of  reflex. 

This  view  is  in  accord  with  many  introspections  in  the  present 
investigation.  Some  of  the  observers  allege  that  they  are  not  able 
to  tell  whether  the  second  tone  is  higher  or  lower  until  they  re- 
produce the  tones  either  audibly  or  mentally  in  terms  of  vocal 
strain.  In  one  individual  test  the  observer,  a  university  student,  was 
not  able  to  distinguish  a  smaller  difference  than  20  v.d.  by  merely 
listening  to  the  tones.  When  he  was  told  to  hum  the  tones,  he 
immediately  ran  down  to  8  v.d.  and  continued  to  improve,  reaching 
2  v.d.  Singing  seems  to  enhance  the  power  of  discrimination  partly 
on  account  of  the  timbre  of  the  voice  and  partly  on  account  of  the 
motor  elements  in  vocalization.  "I  carry  the  first  tone  over  and 
when  I  hear  the  second  I  hum  it  to  see  whether  I  feel  more  or  less 
strain  in  the  vocal  cords." 

These  muscular  and  kinaesthetic  sensations  are  not  always  con- 
fined to  the  vocal  cords.  They  may  start  in  the  vocal  cords  and 
spread  to  other  organs ;  as,  for  example,  "A  strain  starts  in  the 
vocal  cords  and  runs  up  through  my  head."  The  sensations  may  be 
initiated  in  other  organs,  or  they  may  be  felt  as  general  bodily 
changes.  "I  feel  the  tone  as  a  singing  in  my  head."  "In  case  of 
the  high  tone,  the  singing  is  'stronger'  than  in  the  case  of  the  low." 
"The  high  tone  seems  to  make  a  stronger  impression  in  my  ears 
than  the  low  tone."  By  impression  the  observer  probably  means 
muscular  strain.  'T  feel  the  tones  as  vibrations  in  the  body. 
They  seem  to  go  all  through  me  and  cause  a  sort  of  strain."  "I 
have  a  tendency  to  breathe  more  deeply  for  the  low  tones."  "The 
high  tones  give  me  a  sense  of  elation ;  I  seem  to  mount.  The  low 
tones  seem  to  give  me  an  experience  of  gentle  relaxation,  a  general 
feeling  of  calm."  "I  have  a  distinct  tendency  to  move  up  and  down 
according  as  the  second  tone  is  high  or  low."    "Low  tones  seem  to 


EFFECT  OF   TRAINING  IN  PITCH  DISCRIMINATION         89 

drag  me  down;  high  tones  seem  to  Hft  me  up."  "I  feci  an  upward 
impulse  and  tend  to  rise  with  the  high  tone."  "The  mind  seems 
to  be  a  little  more  tense  for  high  than  for  low  tones."  The  affec- 
tive quality  of  the  tone  is  often  the  important  element  in  conscious- 
ness. "When  the  low  tone  follows  the  high  tone  it  seems  to  be 
more  pleasing."  "The  high  tones  feel  different  but  I  can  not  explain 
the  dift'erence." 

In  most  instances  the  auditory  and  kinaesthetic  sensations  com- 
bine into  an  auditory-vocal  perception.  Thus  the  judgment  is  a 
highly  complex  process  conditioned  by  a  mass  of  auditory  and  mus- 
cular sensations.  The  total  result  in  consciousness,  however,  is  a 
simple  experience,  a  mark  of  familiarity  which  enables  the  observer 
to  interpret  the  difference  immediately. 

In  addition  to  sensory  processes  the  judgment  is  conditioned  by 
certain  associational  processes,  chiefly  auditory  and  visual  images 
together  with  certain  associations  which  are  built  up  around  these. 

Many  speak  of  carrying  over  the  memory  of  the  first  tone  and 
comparing  the  second  tone  with  it  through  auditory  imagery.  The 
clearness  of  the  image,  and  hence  the  certainty  of  the  judgment, 
depends  upon  whether  the  interval  is  short  or  long.  This  varies 
somewhat  with  different  individuals  as  does  also  the  character  of 
the  imagery.  Some  observers  associate  certain  familiar  tones  with 
the  image  of  the  present  tone.  The  low  tone  sounds  like  the  "hoot 
.of  an  owl."  The  high  tone  is  associated  with  the  major  key  and 
the  low  with  the  minor  key,  or  perhaps  the  observer  imagines  he 
hears  his  own  voice  singing  the  tones. 

Visual  imagery  includes  localization  in  space,  voluminousness, 
and  color-tone  qualities.  "The  high  tone  seems  to  glide  up  at  the 
end."  "High  tones  seem  nearer  and  low  tones  farther  away." 
"I  have  a  visual  image  of  a  teeter  board."  "High  tones  seem  to  be 
in  the  upper  part  of  my  head;  low  tones  in  the  lower  part."  "I 
think  of  ti,  do,  or  do,  ti  in  the  musical  scale."  This  observer  was 
unable  to  describe  the  tones  in  terms  of  auditory  imagery.  "The 
high  tone  appears  to  be  higher  up  in  space  than  the  low."  This 
reply  is  typical  of  a  large  number  and  seems  to  play  an  important 
role  in  the  perception  of  difference.  "The  high  tone  has  a  swelling, 
expansive  feel  in  the  left  ear  and  seems  to  have  a  pull  upwards,— a 
lifting  quality— almost  to  the  point  of  unpleasantness  in  strength. 
The  lower  tone  seems  to  be  located  in  the  right  of  the  direction  of 


90  FRANKLIN  O.  SMITH 

the  head  and  below.  The  high  tone  is  nearer  the  head,  the  low  tone 
far  away." 

In  the  following  case  the  method  of  localization  is  unique.  The 
relative  position  of  the  two  tones  is  the  reverse  of  what  is  usually 
found.  "The  low  tone  appears  to  be  above  the  high  in  space.  It 
is  also  larger  so  that  the  two  tones  would  be  represented  by  a  heavy 
above  a  light  line,  thus :  ••■iS^SI" 

Many  observers  refer  the  tones  to  a  musical  scale  or  musical  in- 
strument. M.  O.  thinks  how  she  would  play  the  violin  to  produce 
the  different  tones.  H.  S.  sees  her  finger  move  up  and  down  the 
violin  string.  O.  S.  says,  "When  I  think  of  the  second  tone  as  higher 
I  think  of  it  as  higher  up  on  the  piano."  Another  says,  "I  seem  to 
see  my  fingers  moving  along  the  violin  string." 

M.  C.  W.,  a  trained  psychologist,  locates  the  tone  by  a  peculiar 
kinaesthetic-visual  imagery.  The  high  tones  go  up  to  the  right  and 
lie  in  the  head,  the  low  tones  move  down  to  the  left  and  lie  near  the 
left  side  of  the  root  of  the  tongue.  The  first  sound  is  in  the  aural 
axis,  a  little  to  the  right.  All  are  thought  of  as  in  the  head,  though 
she  knows  the  real  source. 

"High  tones  seem  long  and  pointed  while  low  tones  seem  big 
and  flat."  M.  describes  the  interval  as  a  pyramid  or  cone  with  the 
high  tone  at  the  apex  and  the  low  at  the  base.  For  W.  "High  tones 
are  fine  and  sharp.  They  seem  thin  and  compact :  I  imagine  an  ob- 
ject contracting.    Low  tones  are  relatively  rich." 

Colored  hearing  plays  an  important  part  in  the  judgment  of  some 
observers.  Mortiz  Katz*  has  reported  on  color  impressions  of  Schu- 
mann, Tieck,  Liszt  and  others.  In  the  present  study  the  follow- 
ing are  noted:  "The  high  note  seems  to  be  a  brighter  color,  the 
low  darker."  "High  tones  are  bright  and  clear;  low  tones  are 
dark  and  murky."  M.  always  thinks  of  sounds  in  terms  of  color. 
Her  impressions  are  remarkably  complex  and  varied.  "When  I 
hear  sounds  that  please  me  they  appear  violet.  When  I  am  talking 
with  any  one  whose  voice  is  pleasing,  I  see  violet  color.  When 
I  listen  to  a  soprano  solo  I  see  a  section  of  the  rainbow.  As  the 
tones  become  higher  they  change  to  bright  green  and  the  very  highest 
tones  appear  like  little  flames  of  fire.  Low  tones  are  reddish  brown. 
Any  rasping  or  disagreeable  sound  appears  red  or  brown.  When 
I  hear  a  chorus  of  mixed  voices  or  an  orchestra  there  seems  to  be  a 
large  mass  of  violet  color  and  from  this  on  all  sides  little  short 

*Zcit5clir.  f.  angew.  Psychol.,  191 1,  pp.  1-53. 


EFFECT  OF   TRAINING  IN  PITCH  DISCRIMINATION         91 

tongues  of  various  shades  of  green,  yellow,  and  red."  She  does  not 
remember  when  she  did  not  translate  sounds  in  this  way.  L.  M.,  17 
years  old,  combines  spacial  and  brightness  qualities  with  tones.  A 
very  high  tone  appears  to  be  a  bright  vertical  line.  As  the  pitch 
is  lowered  the  line  grows  in  width,  but  diminishes  in  brightness. 

As  regards  the  most  favorable  form  of  attention  we  have  two 
factors,  the  direction  of  attention  and  the  level  of  attention.  As 
regards  the  direction  of  attention  three  modes  are  possible.  One 
may  attend  to  the  beginning,  the  middle  or  the  end  of  the  tone. 
More  than  half  of  all  observers  select  the  middle  of  the  tone  as  the 
critical  point.  The  rest  are  about  equally  divided  between  the  be- 
ginning and  end  of  the  tone.  Closely  connected  with  these  modes 
of  reaction  is  the  snap  judgment.  With  the  organism  set  for  a 
definite  point  in  the  tone,  the  judgment  is  made  the  instant  this  point 
reaches  the  focus  of  consciousness.  This  form  of  judgment  when 
once  brought  under  control  almost  always  favors  improvement. 

It  is  also  observed  that  it  is  easier  to  judge  which  tone  is  higher 
or  lower  if  the  forks  are  presented  abruptly.  If  the  tone  swells 
gradually  from  a  faint  beginning,  it  appears  to  raise  the  pitch  slightly 
and  thus  confuses  the  judgment. 

The  most  favorable  level  of  attention  varies  with  different  indi- 
viduals. The  introspections  show  that  for  some  the  closest  attention 
to  the  tones  is  required  for  successful  work.  Others  say  the  very 
keenest  attention  causes  high  nervous  strain  which  leads  to  mistakes. 
The  writer  has  observed  this  very  definitely  in  his  own  case. 
T.  F.  V.  says,  "Much  depends  upon  my  attitude.  If  I  hold  myself 
in  a  passive  attitude  and  answer  with  ease,  in  a  reflex  way,  I  am 
quite  sure  to  be  correct  in  my  judgmgent;  but  if  I  get  the  attitude  of 
strict  attention  I  cannot  do  so  well.  If  I  can  keep  in  a  state  of 
relaxation,  I  experience  no  difficulty  in  giving  the  judgments." 
Practice  usually  results  in  what  Professor  Welton  calls  receptive 
recognition.  When  one  becomes  familiar  with  tones  there  ceases 
to  be  that  active  attitude  of  attention  which  characterizes  the  first 
few  tests.  The  two  tones  are  not  thought  of  separately,  but  the  in- 
terval is  grasped  as  a  whole  and  is  interpreted  by  its  total  eft'ect  in 
consciousness.  The  factors  which  enter  into  the  judgment  do  not 
come  into  consciousness,  but  remain  unconscious.  All  that  the 
observer  can  state  is  that  he  knows  the  instant  he  hears  the  second 
tone  whether  it  is  high  or  low.  There  is  no  consciousness  of  a 
memory  image  and  no  comparison. 


92  FRANKLIN  O.  SMITH 

To  determine  the  effect  of  distraction  three  series  of  tests  were 
made.  In  the  first  the  eyes  were  closed  (no  visual  or  motor  distrac- 
tion) ;  in  the  second  the  eyes  were  kept  open  and  allowed  free  move- 
ment (normal  distraction)  ;  and  in  the  third  the  observer  was  requir- 
ed to  trace  a  maze  while  performing  the  test  (regulated  distraction). 

The  effect  seems  to  be  about  equally  distributed  between  helping 
and  hindering.  All  but  two  were  appreciably  aided  by  distraction 
at  the  beginning  of  the  series.  At  the  close  only  two  were  especially 
aided  and  only  one  found  distraction  a  hindrance.  In  all  the  other 
cases  when  the  distraction  method  became  automatic,  it  ceased  to 
influence  the  results.  Moderate  distraction  seems  to  be  an  aid 
chiefly  as  a  means  of  raising  the  level  of  non-voluntary  attention. 
The  best  form  of  attention  for  a  majority  of  observers  seems  to  be 
a  periodic  fluctuation  between  sharp  and  instant  attention  to  the 
tones  and  complete  diversion  during  the  interval  between  two  pairs 
of  tones.  The  problem  of  distraction  is  an  exceedingly  complicated 
one.  Perhaps  the  most  striking  result  of  this  series  of  tests  was 
the  demonstration  that  distraction  enters  even  when  we  are  most 
expected  to  concentrate  upon  a  single  task.  Table  XII  shows  the 
per  cent,  of  right  judgments  with  and  without  distraction. 


TABLE  XII 

.    The  effect 

of  distraction 

With 

Without 

Observer 

Distraction 

Distraction 

I 

93-9% 

92.3% 

2 

86.2 

84.5 

3 

89.0 

91.3 

4 

91.2 

87.4 

5 

90.8 

87.5 

6 

88.7 

92.6 

7 

86.8 

91.S 

8 

95.8 

96.3 

9 

92.5 

91-5 

10 

93-3 

97.3 

The  following  extracts  from  introspections  illustrate  the  general 
mental  attitude  toward  the  different  methods.  These  were  written 
at  the  close  of  the  series  of  tests  and  express  the  observer's  im- 
pression at  the  time. 

D.  A.  A.  "In  the  beginning  of  the  test  I  felt  distinctly  dissatisfied  with 
surroundings  and  was  annoyed  by  the  peculiar  eflfect  the  room  had  on  the 
quality  of  the  tone.  This  was  overcome  in  about  twenty  minutes.  The  maze 
failed  to  arouse  interest  and  hence  was  of  no  assistance — quite  the  contrary, 
it  was  really  an  annoyance — a  distraction  unfavorable.  During  the  time  I 
took  100  with  eyes  closed  I  was  able  to  inhibit  any  absorbing  interest  in 
anything    except   the   discrimination    of   tones.     I   was   able   to   concentrate 


EFFECT  OF   TRAINING  IN  PITCH  DISCRIMINATION        93 

very  definitely  on  the  work  in  hand.  Following  immediately  with  closed 
eyes  on  a  test  with  0.5  v.d.  I  grew  tired  of  the  uniform  method  (eyes  closed) 
making  two  mistakes  in  the  first  50  and  six  in  the  second  50.  About  five  of  the 
errors  were  attended  by  a  feeling  of  decided  uncertainty  and  the  others  were 
caused  by  some  annoyance.  Returning  to  the  use  of  the  maze  for  the  last 
100,  0.5  v.d.  I  voluntarily  renewed  interest  in  the  affair  and  raised  my  record 
making  but   four  errors   in   the   100  judgments." 

J.  E.  B.  "At  first  the  maze  troubled  me,  but  after  going  over  it  a  number 
of  times  I  could  do  it  rather  automatically  so  that  more  and  more  attention 
•was  given  to  the  tones.  When  the  eyes  were  open  there  were  always  num- 
erous disturbances  that  would  effectively  distract  attention.  With  the  eyes 
closed   there  was  very  little   to   distract  attention." 

M.  C.  "Working  at  too  great  tension  seemed  to  be  my  greatest  diffi- 
culty during  the  tests,  especially  with  eyes  closed  and  eyes  opened.  The 
maze  seems  to  relieve  that  tension  though  I  rather  expected  the  opposite 
effect.  As  a  result  of  the  tension  I  found  myself  confused  at  times  and  made 
several  errors  in  succession.  I  could  not  notice  much  difference  in  my 
own  attitude  toward  the  test  with  eyes  closed  and  that  with  eyes  open> 
Possibly  there  was  a  greater  effort  to  center  attention  on  the  two  sounds 
when  my  eyes  were  open.  In  both  of  these  tests  there  were  times  when  T 
seemed  to  notice  a  difference  in  pitch,  but  could  not  tell  which  sound  was. 
higher.    This  difficulty  seemed  to  disappear  with  the  maze  test." 

N.  E.  G.  "I  felt  that  it  was  much  easier  to  decide  with  my  eyes  closed^ 
than  with  the  maze.  However,  my  third  record  shows  fewer  errors  with  the- 
maze." 

P.  H.  H.  "In  the  test  using  the  maze  it  seemed  easier  to  concentrate  the 
mind ;  that  is,  the  mind  was  concerned  with  two  definite  things :  the  maze 
and  the  tones,  as  opposed  to  the  free  associations.  There  was  less  inclina- 
tion to  drift  to  other  things.  The  decisions  in  the  maze  test  involved  less 
conscious  effort  and  seem  to  be  'felt'  rather  than  consciously  formed. 
Errors  in  the  maze  test  often  followed  the  effort  to  locate  the  end  of  the 
pencil  line,  after  it  was  lost  through  the  recording  of  the  introspection.  I 
gained  better  success  by  starting  the  maze  line  ahead  of  the  trial." 

T.  F.  V.  "I  found  in  this  experiment  that  everything  depended  upon  my 
attitude  towards  it.  If  I  had  my  attention  in  high  strain  to  perceive  the 
difference  between  the  tones  and  to  give  a  correct  judgment  my  results  would 
be  very  poor.  However,  if  I  fixed  my  attention  upon  something  else  and  gave 
almost  passive  and  indifferent  attention  to  the  forks  my  judgments  were  far 
more  certain.  When  my  eyes  were  closed  I  attempted  to  focus  my  attention 
upon  the  retinal  light  and  also  attempted  to  complicate  matters  by  means  of 
eye-movement.  That  is  to  say,  I  was  endeavoring  to  center  my  attention  on 
something  other  than  the  forks.  In  the  maze,  the  more  intensely  I  worked 
with  respect  to  accuracy  and  speed,  the  more  clear  seemed  the  distinction 
between  the  forks.  This  focusing  of  my  attention  on  something  else  than  the 
thing  in  hand  was  very  hard  to  do,  especially  after  I  made  one  or  two  mis- 
takes in  close  succession.  If  I  had  not  been  so  desirous  of  getting  correct 
judgments  I  am  sure  my  discriminative  ability  would  have  been  better." 


94 


rRANKLIN   O.   SMITH 


L.  E.  W.  "My  preference  is  for  the  maze,  eyes  open,  next  and  last  of  all 
eyes  closed.  In  the  latter  case  my  mind  is  ever  full  of  visual  and  auditory 
imagery,  rich  and  prolific.  One  moment  I  am  in  my  room  and  can  hear 
the  clicking  of  my  typewriter,  the  next  I  am  singing  some  haunting  air, 
then  I  see  a  paper  on  my  table  I  should  have  brought  with  me  this  morning. 
Sometimes  I  recall  in  auditory  imagery  just  what  the  order  of  the  last  two 
forks  was  and  I  feel  sure  that  I  was  wrong  though  I  had  unconsciously  made 
the  wrong  reply.  The  main  difficulty  with  keeping  the  eyes  closed  is  that 
in  so  doing  I  can't  keep  a  constant  image  or  position  before  me;  my  mind 
refuses  to  remain  a  blank.  Now,  with  eyes  open  I  can  fixate  my  eyes  on 
some  particular  object  and  as  long  as  this  does  not  waver  and  my  thoughts 
and  attention  are  on  the  business  at  hand  I  feel  secure — am  so,  in  fact.  With 
the  maze  I  direct  my  attention  to  one  thing  continuously." 

E.  D.  S.  "Yesterday  I  was  interested  in  the  maze  and  hence  was  distracted 
by  it.  To-day  I  felt  no  such  interest  in  the  maze.  In  the  test  with  eyes 
closed  I  became  interested  in  the  method  of  presenting  the  forks  and  was 
thinking  about  certain  possibilities  of  modifying  the  method.  This  became 
a  distraction  or  rather  a  constant  object  of  attention  and  source  of  error." 

The  second  function  of  training  in  pitch  discrimination  is  the 
acquisition  of  skill  in  listening  to  musical  tones.  Four  factors  are 
involved.  First,  skill  means  raising  the  level  of  non-voluntary  atten- 
tion. The  power  to  concentrate  upon  the  characteristic  acuteness 
or  gravity  of  the  tones  v^ithout  conscious  effort  usually  favors 
correct  judging  and  is  the  end  to  be  sought  in  ear  training.  Swift 
found  that  strained  attention  results  in  distraction,  and  a  number 
of  observers  make  similar  statements  regarding  their  own  experience 
in  distinguishing  tones. 

Second,  skill  means  mechanizing  the  conscious  factors  in  learning 
to  distinguish  differences  in  the  pitch  of  tones.  The  pupil  has 
learned  to  image  the  tones  as  auditory,  auditory-vocal,  kinaesthetic, 
or  motor  qualities.  In  this  process  some  one  or  two  qualities  have 
predominated,  and  the  object  of  ear  training  is  to  form  habits  of 
listening  to,  i.e.,  of  thinking  musical  tones  in  terms  of  their  dominat- 
ing imagery. 

The  third  factor  in  the  acquisition  of  skill  is  interest.  One  of  the 
chief  aims  of  ear  training  should  be  to  enlist  the  pupil's  interest 
in  the  appreciation  of  musical  tones  and  the  enlargement  of  the 
scope  of  apperception  with  reference  to  isolated  tones. 

The  physiological  limit 

Tlie  physiological  limit  is  undoubtedly  considerably  lower  than 
is  indicated  by  the  threshold  which  would  give  75  per  cent,  right 


EFFECT  OF   TRAINING  IN  PITCH  DISCRIMINATION        95 

cases,  as  here  used.  To  demonstrate  this  and,  at  the  same  time,  to 
observe  the  significance  of  the  choice  of  a  particular  increment  in 
the  homogeneous  method,  measurements  were  made  on  seven  good 
observers  whose  threshold  had  been  recorded  as  being  in  the  neigh- 
borhood of  I  v.d.  Four  tests  were  made  on  each  of  the  seven 
observers  at  i,  0.5,  and  0.25  v.d.  with  200  judgments  at  each  unit 
in  double  fatigue  order,  or  a  total  of  800  judgments  at  each  unit. 
From  the  per  cent,  of  right  judgments  the  probable  threshold  with 
75  per  cent,  right  cases  was  computed  by  the  Fullerton-Cattell 
formula. 

Table  XIII  shows  the  difiference  threshold  which  was  required 
to  give  75  per  cent,  of  right  judgments  for  i,  0.5,  and  0.25  v.d. 
respectively. 


TABLE 

XIII 

No. 

I  ■ 

v.d. 

0.5     v.d. 

0.25  v.d. 

v.d. 

v.d. 

v.d. 

I 

.42 

•44 

.49 

2 

.40 

.27 

•23 

3 

1.30 

3.33 

1.30 

4 

1. 10 

1.47 

1. 10 

5 

1.75 

1.47 

1.30 

Average 

.82 

.74 

.60 

6 

1. 00 

1. 00 

7 

1.54 

1.30 

Average 

1.24 

1.17 

The  first  five  observers  had  more  than  fifty  per  cent,  of  right 
judgmients  at  0.25  v.d.;  hence  the  threshold  is  calculated  for  the 
three  increments  of  the  other  cases.  Number  6  got  only  49  and 
number  7  only  46  per  cent,  right  cases  on  the  0.25  increment.  But 
the  significant  fact  is  that  for  both  of  these  persons  the  number  of 
right  judgments  on  0.5  v.d.  was  such  as  to  give  practically  the  same 
threshold  as  was  found  on  i.o  v.d.  Only  one  important  incon- 
sistency occurs  in  the  above  table.  In  the  case  of  No.  3.  the  right 
judgments  at  0.5  give  a  threshold  of  3.33  v.d.  while  at  i  v.d. 
and  0.25  v.d.  the  threshold  is  exactly  the  same. 

Examination  of  the  table  therefore  proves  that  in  the  region  of  the 
average  physiological  limit  the  conventional  threshold  may  be  com- 
puted on  the  basis  of  observations  considerably  below  that  limit 
(here  in  five  cases  out  of  seven)  and  that  the  actual  physiological 
limit  is  always  considerably  below  the  conventional  threshold.  This 
is,  of  course,  analogous  to  what  we  find  in  sight ;  under  exception- 


96  FRANKLIN  O.  SMITH 

ally  favorable  circumstances  we  may  see  a  small,  well  defined  object 
at  a  distance  which,  from  the  nature  of  the  dioptric  system,  repre- 
sents the  physiological  limit  of  acuity  in  vision  but  average  records  of 
acuity  would  ordinarily  designate  a  point  short  of  that  distance. 

Correlations 

From  the  standpoint  of  musical  training  it  is  important  to  know 
how  the  ability  to  distinguish  differences  of  pitch  is  correlated  with 
other  mental  characters,  as  general  intelligence  and  singing  ability. 
In  addition  to  these  we  wish  to  know  whether  brothers  and  sisters 
are  more  closely  correlated  in  ability  to  distinguish  differences  of 
pitch  than  other  children  not  related.  These  questions  are  dis- 
cussed in  their  order. 

For  the  purpose  of  the  correlation  between  pitch  discrimination 
and  general  intelligence  and  singing  ability,  the  data  for  pitch  dis- 
crimination were  obtained  from  the  final  days  of  the  practice  series. 
No  single  absolute  measure  of  general  intelligence  is  possible.  For 
the  present  purpose  the  teachers  were  instructed  to  mark  general 
intelligence  on  the  basis  of  two  criteria,  brightness  and  reliability, 
assuming  these  to  be  of  equal  weight.  By  brightness  is  meant 
quickness  and  accuracy  of  mental  grasp,  or,  in  other  words,  general 
wide-awakeness.  Reliability  is  self-explanatory.  It  is  the  correlate 
of  a  small  mean  variation  for  daily  work.  For  convenience  of 
marking,  these  two  factors  may  be  considered  as  having  equal  weight 
and  may,  therefore,  be  marked  independently  on  a  scale  of  lo.  It 
was  explained  that  the  markings  should  follow  approximately  the 
normal  distribution  for  each  age  and  for  both  sexes.  The  mean  of  the 
two  marks  was  taken  as  the  mark  representative  of  intelligence. 

In  order  to  facilitate  correlation  the  ten  units  in  the  series  of  in- 
crements used  in  pitch  discrimination  were  translated  into  corres- 
ponding values  on  the  scale  of  lo,  thus:  30  v.d.  corresponds  to  i  ; 
23  to  2;  17  to  3 ;  etc 0.5  v.d.  to  10. 

The  markings  on  singing  ability  were  also  based  on  the  teacher's 
judgment  of  the  pupil's  ability  to  sing  correctly  in  pitch  scale  and  a 
melody. 

As  regards  kinship,  three  correlations  were  as  follows:  (i)  be- 
tween younger  and  older  brothers  and  sisters  with  practice;  (2) 
the  same  without  practice;  and  (3)  between  the  younger  members 


EFFECT  OF   TRAINING  IN  PITCH  DISCRIMINATION        97 

of  the  second  correlation  and  other  children  of  the  same  age  and 
sex  as  the  second  members,  but  not  related. 

The  correlations  were  determined  by  the  Pearson  product- 
moments  method.  In  order  to  show  the  relative  distribution  of 
individuals  for  each  factor  correlated,  each  group  is  subdivided  into 
five  grades.  This  is  not  a  quintile  subdivision  as  there  is  no  attempt 
to  have  an  equal  number  of  persons  in  each  subdivision.  The 
distribution  by  grades  serves  the  purpose  of  comparison  quite  as 
well  as  the  quintile  or  quartile  method  and  avoids  the  necessity  of 
ranking,  which  is  practically  impossible  on  a  scale  of  lO  units.  The 
method  of  subdivision  is  very  simple.  The  scale  of  lO  units  is 
is  divided  into  five  equal  parts,     i  and  2  =  E.    3  and  4  =  D.    5  and 

6  =  C.  7  and  8  =  6.  9  and  10  =  A.  An  example  will  make 
clear  the  method.     An  observer  gets  3  in  pitch  discrimination  and 

7  in  general  intelligence.  He  belongs  to  Grade  D  in  the  first  factor 
and  in  Grade  B  in  the  second  factor.  The  number  who  are  in  the 
same  grade  in  each  factor  indicates  the  degree  of  correlation.  The 
number  who  are  in  different  grades  in  the  two  factors  indicates  lack 
of  correlation  or  low  correlation. 

The  results  show  a  relatively  high  coefficient  of  correlation  between 
pitch  discrimination  and  general  intelligence,  singing  ability  and 
musical  training  (Tables  XIV  and  XV).  It  is  higher  for  boys  than 
for  girls  and  highest  for  both  boys  and  girls  between  pitch  dis- 
crimination and  general  intelHgence. 

TABLE  XIV.     Correlation  of  pitch  discrimination  with  general  intelligence 

and  singing  ability 
Pitch  discrimination  with 

(i).  General    intelligence       Boys     r  .70  p.e.  .023 

Girls     r  .62,  p.e.  .026 

(2)    Singing    ability                  Boys     r  .71  p.e.  .023 

Girls     r  .51  p.e.  .031 

TABLE  XV.     A.     Pitch  discrimination  and  general   intelligence 

Girls 
Intelligence 
274      A       B       C       D       E 
A        6      14      14 
B      12      51      27        3 
Pitch  C      II       49      2,7      1-2 
D        4        3       17        4 
E  163 


Boys 

II 

titelligence 

234 

A 

B 

C 

D 

A 

4 

15 

16 

3 

B 

6 

31 

29 

3 

Pitch      C 

3 

25 

2,2, 

II 

D 

8 

19 

8 

E 

I 

4 

4 

9 

FRANKLIN   O.   SMITH 


B. 

Pitch  discrimination 

and  singing 

ability 

Boys 

Girls 

Singing 

Singing 

234 

A 

B 

C 

D       E 

2/4 

A        B 

C 

D 

A 

5 

7 

3 

2 

A 

II         21 

12 

I 

B 

1/ 

22 

13 

8        4 

B 

8      46 

38 

10 

Pitch      C 

4 

24 

23 

12          7 

Pitch  C 

8      27 

39 

16 

D 

2 

13 

i6 

8        6 

D 

3        8 

16 

2 

E 

I 

4 

IS 

8      II 

E 

The  fact  of  a  high  correlation  between  pitch  discrimination  and 
general  intelligence  favors  the  conclusion  reached  above  that  pitch 
discrimination  depends  partly  upon  the  ability  to  learn,  i.e,  upon 
brightness  and  reliability.  If  this  is  a  correct  view,  training  in  pitch 
discrimination  is  essentially  mental  training.  It  is  more  than  repro- 
ducing tones ;  it  is  thinking  tones.  Another  conclusion  which  is  in 
harmony  with  what  has  just  been  said  is  that  a  child  may  possess 
a  perfect  ear  for  tones,  and  still  be  unable  to  distinguish  differences 
in  pitch.  Musical  training  should  begin  with  training  in  tone 
quality. 

The  coefficient  of  correlation  between  pitch  discrimination  and 
singing  ability  is  technically  high.  A  high  correlation  between  these 
factors  means  that  the  ability  to  distinguish  differences  in  the  pitch 
of  tones  is  an  essential  factor  in  learning  to  sing. 

Table  XVI  shows  that,  for  the  groups  compared,  girls  are 
superior  to  boys  in  pitch  discrimination,  since  there  are  no  girls  in 
Grade  E  and  relatively  few  in  Grade  D.  But  they  are  not  shown 
to  be  essentially  superior  in  singing  ability. 

TABLE    XVI.      Correlations    for    blood    relationship 

Correlation  between  pitch  discrimination  of 
(i).  Brothers  and  sisters: 

(a)  with    practice  r      .48      p.e.      .031 

(b)  without  practice        r       .43      p.e.       .035 
(2).  Children  not  related         r      .53      P-e.       .030 

The  coefficient  of  correlation  between  brothers  and  sisters  on  the 
basis  of  ability  in  pitch  discrimination  is  not  higher  than  between 
other  children.  This  is  true  both  for  records  without  practice  and 
records  after  practice.  Although  the  results  are  clearly  negative, 
no  sweeping  conclusion  should  be  drawn  because  several  variables 
are  involved,  such  as  advantage  of  the  knowledge  which  comes 
with  age,  differences  in  intelligence,  the  element  of  competition,  etc. 
This  is  regrettable  since  it  had  been  definitely  hoped  and  planned 


EFFECT   OF   TRAINING  IN  FITCH  DISCRIMINATION        99 

that  this  large  collection  of  data  might  contribute  to  tlie  solution  of 
this  interesting  question.  Finally,  the  younger  member  of  each 
pair  in  the  second  correlation  was  compared  with  another  child  of 
the  same  age  and  sex  as  the  second  member,  but  not  related.  The 
coefficient  of  correlation  is  practically  the  same  for  the  three 
groups.  (Table  XVII).  No  conclusions  can  be  drawn  from  these 
meager  results  as  regards  the  influence  of  heredity  on  tonal  hearing. 


XVII.     Correlation   of 

pitch   discrimination 

/o; 

and  older  brothers  and  sisters 

[a)  With  practice 

Older 

129 

A        B 

C 

D 

E 

A 

7        5 

I 

I 

B 

9      2,2 

12 

5 

I 

Younger     C 

4       17 

7 

4 

2 

D 

9 

2 

3 

E 

3 

2 

2 

I 

(2)  Without  practice 

Older 

275 

A       B 

C 

D 

E 

A 

2       13 

12 

7 

I 

B 

2        6 

17 

12 

I 

Younger    C 

12      12 

54 

27 

ID 

D 

7        8 

25 

32 

5 

E 

I        I 

2 

4 

2 

(3)   Children  not  related  and  wi 

thout 

practice 

Older 

275 

A       B 

C 

D 

E 

A 

4 

2 

3 

B 

6      22 

28 

12 

8 

Younger    C 

6      38 

2(> 

15 

9 

D 

2      15 

22, 

4 

2 

E 

13 

16 

4 

7 

General  conclusions 
The  quantitative  statement  and  analysis  of  data  has  been  presented 
in  such  condensed  form  that  a  summary  of  conclusions  from  that 
point  of  view  is  scarcely  necessary.  There  is,  however,  need  of  a 
statement  of  "general  conclusions"  from  the  point  of  view  of  inter- 
pretation and  application  of  the  experimental  results  in  the  light  of 
the  quantitative  data,  the  introspections  of  the  observer,  the  daily 
notes  of  the  experimenter,  and  a  general  study  of  the  problem  with 
the  collaborators  in  research.  Such  a  statement  necessarily  involves 
something  of  a  personal  equation  and  I  am  glad  to  acknowledge  in 
this  the  co-operation  of  Professor  Seashore  whose  long  and  varied 
experience  in  this  field  of  research  makes  this  interpretation  possible. 


100  FRANKLIN  O.  SMITH 

The  psychological  limit  in  jiitch  discrimination  is  always  below  the 
conventional  threshold  (75  per  cent,  right  cases).  Thus,  a  person 
whose  threshold  is  i  v.d.  may,  under  extraordinarily  favorable  cir- 
cumstances, hear  as  small  a  difference  as  .25  v.d. ;  and  it  is  probable 
that  in  the  normal  unreflective  and  uncritical  appreciation  of  music 
the  automatic  "impression"  of  tone  differences  comes  freely  through 
this  region  of  increments  which  are  below  the  conventional  thresh- 
old. This  conventional  threshold  which  can  not  be  further  reduced 
by  instruction  or  training  we  have  called  the  "approximate"  physio- 
logical threshold.  This  is  the  concept  of  threshold  that  must  be 
employed  for  most  purposes  of  research  and  in  nearly  all  applications 
of  the  test  for  practical  purposes.  The  three  factors  which  differen- 
tiate it  from  the  true  physiological  threshold  are — the  convention  of 
counting  75  per  cent,  right  cases,  the  physical  variation  in  the  organ 
of  Corti,  and  the  failure  to  keep  all  the  conditions  of  the  measure- 
ments under  control. 

Success  in  making  a  true  measurement  on  an  unexperienced  ob- 
server in  a  single  sitting  varies  with  the  knowledge,  keenness,  and 
care  of  the  observer  and  the  many  objectively  favorable  or  unfavor- 
able conditions  of  the  test  as  well  as  the  experimenter;  but,  every- 
thing taken  into  account,  it  is  safe  to  say  that  when  an  individual 
test  is  made  under  favorable  conditions  the  approximate  physiologi- 
cal threshold  may  be  reached  in  a  single  sitting  of  less  than  an  hour 
for  more  than  half  of  the  cases  of  adults  or  children  who  are  bright 
and  old  enough  to  understand  the  test.  Even  in  group  tests  by  the 
heterogeneous  method  one  may  reach  in  an  hour  the  approximate 
physiological  threshold  of  nearly  half  of  the  observers  who  are  old 
enough  and  bright  enough  to  observe. 

A  cognitive  threshold,  always  above  the  approximate  physiological 
threshold,  may  be  due  to  failure  in  understanding  what  is  required 
in  the  test,  lack  of  information,  defect  in  auditory  imagery  and 
memory,  lack  of  application,  confusions,  objective  or  subjective 
disturbances,  expectations,  inhibitions  in  writing  or  speaking,  etc. 
Most  of  these  conditions  are  such  that  they  may  be  removed  by  in- 
formation, by  inducentent  to  use  the  best  eft'ort,  or  by  learning 
through  some  experience. 

There  are  means  of  determining  when  the  approximate  physiologi- 
cal threshold  has  been  reached.  Chief  among  these  are  the  mean 
variation  and  the  character  of  the  distribution  of  the  errors.     But  in 


EFFECT  OF  TRAINING  IN  PITCH  DISCRIMINATION        loi 

individual  tests  many  direct  observations  on  the  character  of  the 
difficulties  in  judging  may  be  helpful.  In  general,  vi^here  a  record 
is  low^  (good)  the  chances  are  that  the  observer  has  no  "cognitive" 
difficulties.  The  uncertainty  is,  of  course,  always  with  reference  to 
the  poor  record.  Practical  advice  or  recommendation  should  there- 
fore be  cautious  in  the  case  of  poor  records  for  fear  that  the  limit 
reached,  although  persistent,  may  be  merely  cognitive.  One  can  not 
err  on  the  side  of  getting  too  good  a  record ;  the  danger  is  always 
that  something  has  prevented  a  fair  test  of  actual  ability. 

The  sensitiveness  of  the  ear  to  pitch  difiference  can  not  be  im- 
proved appreciably  by  practice.  There  is  no  evidence  of  any  im- 
provement in  sensitiveness  to  pitch  as  a  result  of  practice.  When  a 
person  shows  a  cognitive  threshold  practice  ordinarly  results  in  a 
clearing  up  of  the  difficulties  which  in  the  way  of  a  true  measure  of 
discrimination  by  information,  observations,  and  the  development  of 
interest,  isolation  of  the  problem  in  hand,  and  more  consistent  ap- 
plication to  the  task  in  hand.  This  is,  of  course,  not  improvement  in 
the  psycho-physic  ear  but  merely  a  preliminary  to  a  fair  determina- 
tion of  the  psycho-physic  limit.  It  follows  that  instruction  in  regard 
to  the  nature  of  the  test  and  individual  help  are  all  important  for 
the  lowering  of  the  cognitive  limit  and  that  mere  practice  for  this 
purpose  is  a  poor  and  uncertain  makeshift.  It  also  follows  that  a 
"cognitive"  threshold  is  no  measure  at  all  but  rather  a  confession  that 
the  measurement  has  not  yet  been  successfully  made. 

Training  in  pitch  discrimination  is  not  like  the  acquisition  of 
skill,  as  in  learning  to  read  or  to  hear  overtones.  It  is  in  the  last 
analysis  informational  and  the  improvement  is  immediate  in  pro- 
portion to  the  effectiveness  of  the  instruction  or  the  ingenuity  of  the 
observer  and  the  experimenter  in  isolating  the  difficulty. 

Reduced  to  its  lowest  terms  the  question  of  variation  with  age 
may  be  interpreted  to  mean  that  we  have  no  evidence  of  improvement 
in  the  psychological  limit  of  pitch  discrimination  with  age ;  a  young 
child  of  school  age  and  even  younger,  can  hear  pitch  fully  as  keenly 
as  an  adult.  The  amount  in  favor  of  the  adult  shown  in  all  group 
statistics  is  amply  accounted  for  by  the  difficulty  in  making  a  re- 
liable test  on  the  young  and  by  their  lack  of  information.  This 
statement  is  based  primarily  on  two  lines  of  evidence. — the  common 
occurrence  of  fine,  irreducible  records  among  young  children,  and 
the  character  of  the  conditions  which  are  ordinarily  overcome  by 
instruction  and  training. 


102  FRANKLIX   O.  SMITH 

Pitch  discrimination  does  not  vary  with  sex  to  any  significant- 
extent.  In  the  records  here  reported  and  in  the  many  hundreds 
of  other  records  in  this  laboratory  in  which  comparisons  may  be 
made  for  sex,  certain  tendencies  are  shown  in  groups  of  records, 
sometimes  in  favor  of  one  sex  and  other  times  in  favor  of  the  other 
sex,  but  on  the  whole,  it  seems  certain  that  such  differences,  except 
so  far  as  they  are  due  to  grouping,  may  be  accounted  for  as  due  to 
the  conditions  of  the  test  rather  than  to  the  sex  difference  in  the 
psycho-physic  capacity  of  pitch  discrimination.  Thus  one  of  the 
most  consistent  and  striking  differences  reported  above,  that  of  the 
superiority  of  elementary  schoolgirls  over  elementary  schoolboys 
may  probably  be  fully  accounted  for  by  the  prevailing  trait  of  aloof- 
ness of  the  preadolescent  boy  toward  music.  These  boys  often 
regard  music  as  a  sort  of  frill  for  girls  and,  therefore,  enter  the 
test  with  less  fervor  than  do  the  girls.  Such  interpretation  is  sup- 
ported in  part  by  the  fact  that  in  the  high  school  and  in  the  univers- 
ity, where  the  girls  have  had  far  more  advantage  of  training  than 
the  boys,  the  records  reveal  no  appreciable  difference  for  sex. 

Not  a  single  case  of  tonal  deafness  was  isolated  in  any  of  the 
records  here  reported.  This  would  indicate  that  if  tonal  deafness 
exists  at  all  in  a  "normal"  ear,  it  is  no  so  common  as  has  usually 
been  supposed. 

We  have  found  a  high  correlation  between  pitch  discrimination 
and  ability  in  singing,  as  judged  by  teachers.  In  the  collective 
records  there  is  also  a  high  correlation  between  pitch  discrimination 
and  "general  intelligence."  This  is  undoubtedly  due  to  the  presence 
of  so  many  "cognitive"  as  opposed  to  physiological  thresholds. 

Under  the  conditions  of  this  test  the  records  of  members  of  the 
same  family  do  not  correlate  more  closely  than  do  members  of  dif- 
ferent families. 

This  test  is  elemental,  i.e.,  when  applied  under  favorable  condi- 
tions it  calls  forth  a  relatively  simple  and  immediate  sensory  dis- 
crimination which  does  not  improve  appreciably  with  practice. 
It  is  like  the  minimum  visible  angle  in  visual  space — the  limit  is 
set  by  the  sense  organ.  We  say  "under  favorable  conditions" 
because  the  cognitive  factors  which  condition  a  fair  test  must  be 
recognized.  As  has  been  seen  in  a  large  per  cent,  of  cases,  we 
can  get  only  a  cognitive  threshold  in  the  first  attempts.  As  elemental, 
this  test  is  contrasted  with,  e.g.,  a  test  of  ability  to  isolate  overtones 


EFFECT  OF  TRAINING  IN  PITCH  DISCRIMINATION        103 

in  a  violin  tone  which  represents  a  skill  that  can  only  be  acquired 
through  practice.  It  must  be  recognized  that  the  test  is  a  true 
and  successful  test,  the  results  of  which  may  be  applied  with  safety, 
only  as  it  is  actually  elemental. 

The  basal  character  of  pitch  discrimination  in  the  appreciation 
and  expression  of  music  has  become  evident  in  many  ways.  Keen 
recognition  of  pitch  difference  is  a  condition  of  auditory  imagery, 
auditory  memory,  singing  or  playing  in  true  pitch.  This  is  true  as 
well  for  the  affective  attitudes  with  reference  both  to  pitch  and 
to  timbre,  for  timbre  is  in  the  last  analysis  simply  a  pitch  complex. 
It  would  therefore  seem  to  be  most  fundamental  of  all  tests  of 
musical  talent,  although,  of  course,  no  one  test  by  itself  can  be 
considered  an  adequate  rrieasure  of  such  talent. 

The  educational  value  of  this  test  has  been  strongly  impressed 
during  this  work.  It  is  unquestionably  the  isolation  and  measuring 
of  one  specific,  basal  factor  in  musical  talent.  It  may  be  under- 
taken individually  or  in  groups  and  commends  itself  particularly 
as  one  of  the  tests  that  should  be  made  in  schools  for  the  purpose 
of  vocational  guidance  in  music,  in  the  music  studio  for  the  pur- 
pose of  learning  where  to  place  the  emphasis  in  instruction  and  in 
adapting  the  course  to  the  natural  capacities  of  the  student,  and 
as  a  recurrent  exercise  in  the  schools  and  in  the  studio  for  the 
purpose  of  developing  keenness  in  attention  to  detail  of  tone  in  ear 
training. 

The  instruments,  i.e.,  the  tuning  forks  and  resonators  as  here 
used,  and  the  method,  both  the  heterogeneous  and  the  homogeneous 
procedure,  have  proved  eminently  satisfactory. 


THE  LOWER  LIMIT  OF  TONALITY 

BY 
THOMAS    FRANKLIN    VANCE 

An  accurate  determination  of  the  threshold  of  the  lowest  audible 
tone  involves  a  consideration  of  the  variables  which  condition  it. 
The  area  and  the  amplitude  of  the  wave  and  the  distance  of  the 
vibrating  body  from  the  ear  of  the  observer  are  the  principal  objec- 
tive variables.  Individual  differences,  due  largely  to  innate  capacity, 
degree  of  practice,  and  ability  to  concentrate  attention,  and  varia- 
tions within  the  same  individual  which  may  be  attributed  to  changes 
in  physical  tone  and  mental  content,  are  obviously  the  most  influen- 
tial subjective  variables.  These  variables,  both  objective  and 
subjective,  present  particular  problems  which  must  be  considered 
in  their  relation  to  the  general  problem  of  the  lower  tonal  limit 
before  the  latter  can  be  accurately  determined. 

No  attempt  will  be  made  here  to  review  the  history  of  investiga- 
tion on  this  problem.  A  good  summary  is  found  in  Titchener's 
Instructor's  Manual,  Quantitative. 

Mr.  Misao  Imai  made  a  careful  study  of  this  problem  in  this 
laboratory  in  1907.  Inasmuch  as  his  results  have  not  been  published 
and  the  present  study  is  essentially  a  repetition  of  his  work  for  the 
purpose  of  verification  it  is  necessary  to  report  his  work  in  brief. 

Mr.  Imai's  first  problem  was  to  determine  the  relation  between  the 
threshold  and  the  amplitude  of  the  wave.  He  produced  the  tones 
by  an  electro-magnetic  fork  460  mm.  in  length  and  10  mm.  by  20 
mm.  in  cross  section  of  a  prong.  By  differential  weights  five  tones 
could  be  produced,  namely,  35,  25,  22,  19,  and  17  v.d.  By  varying 
amount  of  resistance  different  amplitudes  could  be  secured.  The 
test  ir«.  each  caise'coiisiisted  in  determining  the  smallest  amplitude  that 
would  produce  an  audible,  tone  at  a  given  pitch.  The  measure- 
m,enfsrwere  made -on:  ten  laboratory  students.  With  this  apparatus, 
he  obtained  the  results  shown  in  Table  I. 

TABLE  I.     The  relation  of  threshold  to   amplitude 

v.d.  ampl.  in   mm.  m.v. 

30  1.30                                           .IS 

25  1-73                                           .30 

22  2.20                                           .45 

19  2.95                                           .50 

17  345                                           .50 


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